What about the Romance set?
If I may say something, Romance language speakers have no problem using Spanish/Portuguese/Catalan poder, Italian potere, French pouvoir, Romanian a putea indicating permission or possibility. Slavic language speakers the same.
For Slavic, Russian has for being able to, знать and уметь, and for being allowed to, мочь
I don't see знать as being able to, rather as to know, as in:
Я знаю эту жеищину. "I know this woman."
Я знаю, что ты еще меня любишь. "I know that you still love me."
Interestingly Czech and Polish have two distinctic words for tthat знать: vědět/wiedzieć and znat/znać (cf. Spanish saber vs. conocer, Swedish veta vs. känna):
Cz: Znám tu ženu. Po: Znam tę żonę. "I know this woman."
Cz: Vím (from vědět), že mě ještě miluješ. Po: Wiem (from wiedzieć), że mię jeszcze lubisz. "I know that you still love me."
Macedonian, like Russian, doesn't make that distinction: Ja знам оваа жена/Ja знам женава. Знам дека ме уште сакаш.
Yметь has to do with ability (yм means
mind): Она умеет плавать "She knows how to swim/She can swim."
Mочь has to do with possibility: Я cмогу вам дать ответ завтра "I can give you an answer tomorrow."
For permissions, a dative construction with можнo is very common: Мне можнo курить здесь? "May I smoke here?"
Brazilian dude