I'm interested in conjuration.

Do the weapons get stronger as conjuration levels? Or as the weapon skills level?

Do weapon skills level from conjured weapons?

Can you conjure armor?

Does conjuring level as your beasts/weapons do damage, or only when you summon them?

Tell me all you know, please. If you don't mind :].

Weapon skills do level up with conjured weapons.

Bound Weapons, summoning creatures, and raising dead has to be done in the context of a fight to award experience, and you do not gain additional experience when summons take or deal damage. You can summon a creature, raise the dead, or get a bound weapon, and then enter a fight and still receive experience if your creature/zombie/weapon is still present.

Soul Trap, and Daedra Banishment have to hit a target, and also must not be resisted or have no effect to gain experience. If the Daedra is too strong for your particular spell, you will recieve no experience.

To my knowledge, there are no Bound Armour spells.

Conjured weapons, as far as I can tell, do not scale with your level of Conjuration. They do, however, get more powerful as the associated perks are leveled. For example, a 60% damage increase in the One-Handed tree will affect the damage output of your conjured sword. It appears the base damage of the sword is 22, and I think the bow is around 55.

Your related weapon skills do level based on whatever conjured weapon you're using, yes. Basically, think of a conjured weapon as a normal weapon for skill-purposes.

I haven't heard about conjured armor, nor seen the spell at any of the shops. I'm level 21 and have been to maybe 4 of the major cities, including the mage's college in Winterhold, and haven't seen a "conjure armor" spell.

As far as I can tell, conjuring only seems to level when you cast the spells. However, keep in mind that you'll be constantly re-casting your weapon and oakflesh/stoneskin in most areas where there's potential for you to get attacked. The conjured sword lasts 120sec and takes a few sec to cast, so you don't want to be caught without a weapon in a pinch. I use the conjured sword all the time, with an atronach and stoneskin in close second. The "raise zombie" line is just stupid, I'd recommend against it. It takes a bit to get the zombie on its feet, but what's worse is, he won't grab a weapon until you get attacked. You either have to "plant" his weapon back on his corpse prior to raising, or wait for him to run all the way back and grab his weapon in the middle of a fight.

What else to say... You can make some decent money if you get your Conjure-perk that binds souls to soul gems when using a conjured weapon. Fill your inventory with a bunch of empty gems, then run around harvesting hides (which also fills the gems). Go back to town, turn your hides into leather and smith a bunch of gear, then go enchant it.

The conjured bow is a little abnoxious, despite its high-damage, because you can't cast while wielding. If you need to re-summon a creature, you have to sheath the bow (which destroys it), conjure a creature, and re-cast the bow. Kind of annoying and time-consuming.

Hope that helps!

PS: In my 21 levels, I've only seen a one-handed sword, axe, and bow as far as conjured items are concerned.

Don't put any perks in conjured weapons, they may be good at lower levels, but when you find better weapons later the perks will be useless (as I am painfully aware)

I'm interested in conjuration.

Do the weapons get stronger as conjuration levels? Or as the weapon skills level?

Both.

Do weapon skills level from conjured weapons?

No

Can you conjure armor?

Oblivion yes. Skyrim no

Does conjuring level as your beasts/weapons do damage, or only when you summon them?

Only when summoning

Also, only while in combat.