A few MTW questions

[Ludens]

IIRC, UM are armour peircing and are armed with pole arms. This equals death to cavalry and armoured units, Ghulams are both!

UM are not armed with polearms but poleaxes, making them AP but not anti-cavalry. Also, Mameluks are not heavily armoured and are lacking a bit when it comes to stats. Anyway, it is usually a bad idea to let cavalry make an unsupported frontal attack on infantry, as they get worn down in the following melee. Their low numbers and broad frontage make them vulnerable to be overwhelmed by an unbroken enemy. Cavalry are for charging and breaking a weak or wavering enemy, not for slugging it out in melee. Do not underestimate UM either. They may be militia, but with a little valour they are less likely to run away and they have the stats (plus an AP bonus) to do some damage.

I faced an HRE crusade in battle and set up a 2 valour unit of Muwahid Foot Soldiers on a slightly elevated position three ranks deep and in the hold position. The enemy general Royal Knight unit charged and the impact caused 27 Muwahid Foot Soldiers to fall in less than 3 seconds. Huh? I also had a similar problem in a bridge battle when my Saracen Infantry unit on the bridge lost 30 men before the attacking Royal Knights (similar valour also) lost a single man. What is happening here?

As Lugh explained, Muwahids are fast but lightly-armoured spearmen that tend to die very fast. The Saracens incident can be explained because the Saracens were on a brigde (bunched up and thus suffering a squeeze penalty) and out of formation. Off course, flukes happen sometimes.

I've considered downloading some patches or mods when I tire of vanilla, but are there any recommendations for a certain patch or mod that I should download? Are there any that absolutely needs to be downloaded that makes the gameplay significantly better?

You shoud certainly download the patch (1.1 if you don't have VI, 2.01 if you do) as they solve a lot of issues. I don't know if they cause save game incompatibility, though. I definitely recommend installing VI as well as it strongly improves the game. As for mods, the problem is that there are very few mods for vanilla M:TW. All good ones have been ported to VI long ago. There was a discussion on which mod was best some time ago in the Main Hall. You can find it here.