You're not going to get elite troops of any sort in a hurry, except for ones you rescue from lords and bandit swarms. Top-tier infantry and cavalry are particularly bad, archers are at least a little easier because of the sheer number of kills they tend to rack up each fight, and I'm not dexterous enough at leading my horse archers to get them past their first rank alive anyway so I have no experience there. But seriously, if you're after anything at T7 it's better to look at your target's prisoner column and recruit those, because otherwise you're only ever going to get a slow trickle. T6 units are easier to get and keep, but even there it can be a long slog.
At a guess, the main problem you're probably having with your infantry being slaughtered is the troops you're using. As Vaegirs, your infantry are some of the weakest in the game, with a low cap on armor, okay but slow and short melee weapons (though the blunt damage takes the edge off the enemy's armor), and mediocre shields at best. Your archers and cavalry will have to compensate for that - you've got undeniably the best foot archers around, very powerful but slow horse archers, and excellent shock cavalry with a bit less staying power than the Sarranid or Swadian equivalents. Khergit infantry have an extra tier or two of armor over yours, Nords have obscenely good armor, weapons, and shields, and Swadians tend to make up for middling equipment of their own with massive weapons and high power strike. If you're in a position to train some Rhodoks they can fill the gap, and mercenary infantry are lethally effective and heavily armored, but until then your Vaegir footmen are really just finishers for the cavalry and meat shields for the archers.
You mentioned bandit hunting, and if you're up for it I'd suggest cleaning up Sea Raiders. Mountain Bandits give fairly insignificant amounts of experience, Forest Bandits are a bit better and have some excellent drops, Steppe and Desert Bandits are almost all mounted, give mediocre experience, and tend to instakill unlucky troops with lances while riding circles around them with horsebows (and let's not even talk about the goddamned Black Khergits the Desert Bandits get...), and Tundra Bandits have some scary bows but are otherwise a fairly good farm - plus, if you're a Vaegir, they're in your hometown. Sea Raiders generally have more valuable loot and can be considered as training for fighting Nords, though, so I'd tend to recommend them. Even when you're rolling up noble parties too, fighting bandits can still be a worthy pasttime - after all, they'll intercept villagers and caravans and decrease the rent you get (or the troops your allies get) from provinces.
As for enemy party AI, yeah, it's pretty dense. I've found three behaviors, more or less - the enemy will either swing slowly in a circle around the map until they eventually spiral into your line (which has probably been twisted out of position because of the poor tracking), they'll hold their position and wait for you to walk into their deathtrap (and they've got more patience than you do), or they'll just sound a general charge and you'll end up fighting their archers in melee before their infantry arrive (generally what your allied lords do in large-scale battles, which is incredibly annoying since there's no way to save them). I have no idea what the different triggers are, only that knocking out the lord or a few troops can sometimes trigger a full charge.
Once you own a castle or town, you'll have the option to appoint a...er...I can't recall the title, but he directs garrison and patrol recruitment. You pay up front to make him hire and train groups of new units, which tend to follow a level pattern similar to what AI lords get - a lot of T4s, a decent number of T5s, a very small number of higher tiers (if you're lucky), and a few straggling lower tiers. It happens more or less automatically, but there's some interaction required at first and I forget if the process stops after a while. I tend to play as a mercenary for as long as I can get away with, so my memory on lordship is a bit faulty, sorry.
As for getting that castle or town, they're not just going to hand it over to you. Each kingdom keeps a couple of lordless villages to assign to newcomers, but every castle and especially every town is owned and garrisoned. You want a castle of your own, you're going to have to ride out and conquer it yourself. Vaegir archers make that as easy as it's going to get, at least, since even your low-tier troops have the damage, aim, and rate of fire to massacre a moderately sized garrison from the ground. I'd advise picking a fight with the Khergits first, though, since their horsebows are much less effective in that sort of stand-up fight, while the Nords have their massive shields and powerful throwing weapons and the Swadians have archers only a little bit below your own to retaliate with. Once you complete a siege that you initiated, you can request that the castle be given to you. Most of the time you'll get it, unless you're Controversial from a recent Marshalship or demanding too many other fiefs in a short time. Sometimes it'll be awarded to another lord even when you're an ideal candidate, but those are fairly rare occasions - a popular lord has just lost his land, the king gets selfish and claims it for himself, things like that.
I'm not really certain what else to say right now. I don't think I've ever seen the error you mentioned with the battle resizer, for instance, mine works just fine. Hopefully there are answers to that on other forums. Same with the modding question you brought up - if it affects the amount of experience needed for promotion, then it'll only affect you since lord armies just recruit templates out of thin air (modified by the current wealth of their fiefs), but if it affects the experience gained per kill I have no idea.
I hope I've been able to help a bit! Good luck with your campaign.