I have a couple of noob questions

[Empirate]

On beating the Mongols/Timurids, let me refer you to the most useful thread to date. It's found here.

For a summary, let me just say you need a heavy infantry core, anything that can withstand bowfire and cavalry charges (Pavese Spearmen, Dismounted Feudal/Chivalric Knights, Armored Swordsmen...). You also need lots of long range missile troops (Pavese Arbalests are perfect, any kind of longbows is just fine, too).
Keep your troops together, keep the high ground, whittle the Mongols down with missiles, absorb charges with your melee infantry. Never break formation, don't pursue the enemy, resist all temptations, watch your flanks. Watch your ammo count (!), shoot all your missiles, withdraw in good order when out of ammo and fight again another day.
When you get comfortable with this style of warfare, mix in specialty units for specific purposes: a little cavalry to pursue routers (but draw them back quickly when the enemy reforms), a little siege maybe, a True Cross is immensely helpful. Use good generals to withstand the Mongol generals' high dread ratings. That's basically it.

Enjoy yourself, the Mongol and Timurid invasions are among the most exciting parts of the campaign!