Do I understand correctly that the meaning of "umieć" is limited to "to be able to" and thus does not cover all meanings of "can"?
„Umieć” means "to be able to, because one possess skills or abilities"
„Móc” means "to be able to, because the circumstances allow it"
„Puszka” is a container, typically made of metal and used for storing food with long expiry date
Are you curious about any other translations of the English word "can"?
And then there is the misuse of "can" (to mean "may") meaning "to be allowed to do sth".
Is 'Umiesz pisac list" also fine? Because as I understand it, Perfective is either future tense or past tense and this seems to be neither
This is a present tense, but „napisać” here is used as an infinitive for the modal verb „umieć”.
Perfective and imperfective verbs can be imagined as "completed" and incomplited". If you ask „Umiesz napisać list” then you are asking whether you are able to write a single letter from start to finish, completely. In „Umiesz napisać listy” we have a set amount of letters to be written and we are asking whether someone is able to write them. In „Umiesz pisać listy” you are asking about a general skills for writing letters in general. „Umiesz pisać list” sounds simply not right. It's as if you were asking whether you can pretend you can write a letter in a movie or something.