For this player, sounds to me...there is "denial" and then there is "delusion." This player sounds like they are more steeped in the latter than the former. Or simply a compulsive liar in some misguided attempt/perception to "win" and/or play the game they want/imagine regardless of what is actually happening...in which case, they are welcome to go play by themselves.
We have only a short text description of behavior over the internet. A professional should/would refuse to do a psychiatric evaluation on the basis of this description, and we are certainly less qualified. So, let's not go there, hm?
In addition, we should not ascribe to deep emotional or mental problems what can be fully explained by basic human nature. The player has some desires for their character that are not supported by the rules. Either they lack system mastery and are unaware of this, or they are aware, but want to have their cake and eat it too. You don't need to be delusional or a compulsive liar to attempt to try to wheedle what you want - just a little greedy and self-centered.
For the armor bit - I admit that I tend to cut players some slack. Their characters live in the world 24/7, but the players don't. The players may not think of things the characters certainly would, so that holding them to thinking ahead is often a "gotcha". For things that are honestly perfectly reasonable (like, "Gee, I'm getting on a boat, if I fall in wearing heavy armor, I will probably die!"), I'm willing to retroactively allow them to have bought basic equipment, if they are willing to pay on the spot. If it isn't painfully obvious, or I'm feeling a little mean, I use Wisdom or Intelligence checks - would the character have thought of this, yes or no?
As for the disguise bit - do not blame the player for defending their right to do a thing that has been established that they can do. They were allowed to pass for some time without question - why should that change now? If you are going to enforce the rules on this, it must be with apology: "I'm sorry, I didn't think of this before, but I've allowed you to do things that, by the rules, your character couldn't do. I need to be consistent about the rules, and correct things when we catch errors, so we need to do something about this." Consider allowing the character to swap around points, or allow them this one practiced disguise as a pass while they buy up disguise skill going forward.
Remind the player that they don't get to assert what others think, by the way. That's not appropriate.