What would "so that you can learn czech" be?
Jsme tady, abyste se mohli/y učit česky.
oh, so it is once again this "se" word that swiches meaning of "uci*" from teach to learn ?
Yep, kinda. učit = 'teach', se makes it reflexive, so: učit se = 'teach oneself' = 'learn'
Is "We are here to teach you Czech language" so terribly wrong?
I suggest staying at the adverb.
Also, I think it would have to be "the Czech language".
"the Czech language" sounds better. Thanks