Troubles with Almos and Cumans

[Scurvy]

Against heavy can in early i usually use a unit of spears and l.cav/ha's.

attack the heavy cav with the l.cav and then retreat into the spears, the heavies get caught up in the unit and you can either flank or just leave them to tire themselves out.

[Heidrek]

I know Bashkorts very well, as they formed the backbone of my VB army. things you should know about Bashkorts:

1. They are a polearm unit, so they get +3 Atk and +1 Def against cav.
2. They have weak close combat stats compared to melee units (1 atk, 2 def)
3. They have a shield, but basically no armour so regular arrows will hurt them.
4. Anything getting into melee range will take losses from their javelins, as you found out.
5. They are Fast.

Best way to neutralise them is with Ranged fire. Long range options like Arbalesters are a great idea, but Horse Archers will also do fine. As soon as the enemy heavy cavalry starts coming after your HA's, run them back to your line and send some spears to engage the enemy cav. if they turn and go back to their lines, have the HA's fire off a volley or two at their backs.

With Arb's, just set up camp near the enemy, them march your arb's out in front and start picking them off.

If you have to engage them hand to hand, advance at the charge in loose formation to minimise your losses then go into close when you get into melee range. If you're on defense, go into the woods, jav's a re basically useless there and your infantry will tear them apart.

Once they have used their Javelins up, they are just a bunch of weak Halbardiers. I love Bashkorts, but they have some serious flaws. weakness to ranged fire is one of them.

[Brave]

To kill cav make sure you have a pointy stick or two.

[Great Est.]

To deal with the javs you can also exploit the AI's ill-advised strategy of setting them to skirmish. Charge a horse archer or another light horse such as steppe cav close to them in loose formation and they turn tail. These disruptions can keep them from launching their projectiles effectively, but requires micromanagement and must be paired with archers (arbs hopefully) to do the actual killing.
Alternatively, you can rush your melee (spear and swords) line at the bashkorts and they, again, will try to retreat to their firing range. Your guys should hit their guys in the back. You'll need fast infantry, though, or some horses to "herd" them closer to your lines. The point is, if the javs are on the move, they are not firing.
AI javs pose much less of a threat when the AI uses them in defense since they tend to let them just sit there for your bows to pick apart. So maybe the strategy for you is to take the battle to the enemy.

As for the enemy's heavy cav, if I may echo what others have already said, mounted bows can whittle these bad boys down to manageable size.
You might consider mounting an all-horse army against this Cuman heavy/bashkort enemy. Then you can easily keep away from both javelin and lance and fight on your terms.