1 One other possible source of her insecurity:  She has mentioned several times that she has never completed a "raid" in the game.  That means that she does not have access to the most powerful weapons and armor, and also lacks other items such as the flying griffin mounts that her friends have. 

In many MMOs, raid-level equipment can allow a player to dominate a higher-skilled player who lacks the raid-level gear.  With no raid-level gear of her own, she will always be "second rate" in the world.

2 Ken, I lost your e-mail (if I ever had it), but have a look at the Antares launch visibility map. Norfolk is within the 20 degree inclination zone.

3 Yeah, she's having a professional crisis, more than a personal one. (We're not used to thinking of "am I any good at this game" as a professional crisis, but that's what it is.)

Akatsuki is a classic RP player. She's more interested in her characterization than her character stats. Because of her particular role, she doesn't join up with others easily. A bit of plot contrivance and a sense of obligation that dovetailed perfectly with her RPing got her a spot in the Shiroe-party, and she's established a comfort zone there, and she's REALLY not comfortable outside of it.

To be blunt, aside from a bit of PVP, Shiroe did not get up to any great shakes in combat in the first season. They cleared a relatively low-level dungeon without a healer, they killed some mook goblins low-level enough that the Newbie Party could fight 'em, and... that's it, more or less.

Akatsuki has gotten the impression that raiding is the epitome of character advancement, and in a few ways that's true. She does not have the best equipment. She's got a serviceable set of weapons. But in another sense, she's completely wrong; the best players are NOT raid players. Anyone who's ever run a raid will tell you, you're going to have some really good and dedicated players along, and you're going to have some Demi-demi types who have the skills but not the brains, and... you've got a few slots filled with people who are just skilled enough to Not Stand In The Fire, if you're lucky. (Oh, sure, there's a handful of guilds who can field a good-sized raid full of "pro" players. But most everyone else makes do with what they can get!)

The biggest raid skill is to follow instructions properly and not get yourself killed. Don't Stand In The Fire. It's not topping the DPS chart (in fact, that's kind of a newbie mistake - it's more important to stay within the limits of aggro and, if you're lucky, sustain. The better your gear is, the easier the latter can be.)

It's in a small party that you have to know your stuff, because there's just fewer people to carry you. If there's twenty-five people and one of them Stands In The Fire, oh well, you can probably soldier on (especially if they're one of your newbies, contributing less than the average for their role anyway.) If there's only five and you lose one, it takes a GOOD set of four to keep things up.

The thing is, is Akatsuki worried about being good as a player? Not really - she's worried about not being good at her -character-, which is another thing entirely. And I'd be shocked if this arc doesn't hammer home the difference in a way that gets her over her funk. She's someone who spends a lot of time being a shinobi... which, recall, is not actually her character class, just her conception on how to play her mix of job and subjob. She's definitely using her skills in non-combat situations more than the rest of the cast combined. And if the script calls for someone who can hunt down and slay a crazed swordsman in the shadows of a snowy town, well... that should make for a good dose of self-actualization.

4 1. Given the importance of Shiroe and his guild to Akiba, given Akatsuki's personal and professional importance to Shiroe, and given Shiroe's notoriously encyclopedic knowledge of game mechanics, one must ask why the heck Shiroe wasn't making sure that Akatsuki got some raid experience/goodies (maybe partied up with some of their Crescent Moon or other guild friends). I mean, yeah, they're busy and it's only been a few months, but sheesh. Also, yes, money is tight, but they could have lent/paid Akatsuki money for a new sword. Sheesh. It's a lord's duty to equip his bodyguard, right?

2. Shiroe is apparently not talking to Akatsuki much while away, and actually he seems to have spent a lot less time talking to her ever since he finally realized she was interested in him. This coincided closely with his taking Minori as an apprentice and spending a lot more time talking with her. So yeah, rationally you could say, "Shiroe is just being a little shy with Akatsuki while he works out his own feelings, and he's busy with Minori but may not even notice that Minori has a crush on him, and certainly doesn't take it seriously if he does." But lack of talking and contact would make Akatsuki bound to be a prey to paranoia, romantic depression, and overthinking, unless she were an extremely secure and cheerful  person. Which she's not.

3. Actually, in Japan it's historically been pretty rational to worry about a nearly-middle-aged man deciding to romance a teenager (and of course many fannish Japanese guys at least say they want a schoolgirl). That used to be one of the main marriage patterns, for those who could afford it. Akatsuki has probably read ALL of the first Japanese novel, The Tale of Genji (where Prince Genji's true love is a girl he raised from childhood and marries at puberty, IIRC) , and she knows that there are way too many men and women drooling over her own schoolgirl-age appearance in the game. So while she is probably sure that Shiroe isn't after an underage girl, she can't be absolutely sure; and Minori's mind is as good as anybody's. (And rationally, there are a lot of underage girls who have been known to try seduction in moments of puberty madness, which is the other reason why chaperones are a thing.)

4. Akatsuki is a loner, and therefore probably has either little romantic experience or too much of the bad kind. Akatsuki is also a woman, and frankly, most of us are experts at being insecure and   territorial. You can grow out of one and get more graceful at the other, but Akatsuki doesn't have any female friends or relatives in this world who are close enough to her to be able to talk her down at the moment. (I hope Lenessia takes on this role.)

5. If Akatsuki is almost out of college, she's almost on the verge of becoming "day-old Christmas cake," too old to marry according to society. The way Japanese marriage patterns go, she has a few more years yet, but it's more like three or five, rather than ten. Of course, any friend would tell her that her ageless looks will make age not so important, but it is a rational consideration. Depending on her family, she may have to deal with arranged dates/marriage mixers if she doesn't find a husband herself, and a sensitive soul like Akatsuki would probably die of the embarrassment.

5 In Shiroe's defense, he's clearly working on the gear thing, just as a surprise (and a top-quality, raid-class katana with unique flavor text is obviously the perfect gift for her right now!) Just bad timing that he has to be out of town, etc.

Also, it looks like Shiroe and Naotsugu are in kind of a "been there and done that" situation for raiding, if Naotsugu slots into the main tank role when he's a visiting member for the raid. (In a lot of ways, that's an enormous professional compliment. Main tank is the one job you absolutely cannot finesse or carry - that guy has to have the best possible gear and absolutely has to have the skills too. You don't let someone you don't know main tank unless they're completely, obviously the better option; for a raid guild to let Naotsugu take that role means he is either geared within an inch of the best possible gear, or that he has a near-legendary reputation. Or we found a plot hole...)

And Shiroe's running strategy, not just as "okay, here's what we need to do to bust this boss", but as if he's run progression content before. It's one thing to say "okay, we have installed Deadly Boss Mods and it will show us where the fire will be so we can avoid standing in it" and another thing to say "okay, we need to learn where the fire will be so we can avoid standing in it, and also to get that info to the guys who make Deadly Boss Mods." MOST raiding guilds aren't the kind to soak up the casualties to learn that stuff.

All this might indicate a hole in Shiroe's thinking, though. If he's an ex-raider, he probably has very different opinions on raiding compared to Akatsuki, who's a non-raider. And, well... it's not beyond expectation that the topic just never came up, given that they're both quiet and somewhat unsociable. But if Shiroe thinks "she's already very awesome at what she does," it might not have even occurred to him that she has anything to be insecure about, much less that she actually might be insecure about it.