Both can and be able to can be used to talk about ability. i can teach, am able to teach, the same. but use of (can) can also express possibility (rather than ability) like; q: How could I improve my English? - a: by practice!

You can put "be able to" into any time or grammatical phrase. With "can", you're limited to conditionals and general ability. For example, it's not possible to use "can" in present perfect, but "have been able to" is definitely correct.

"can" it hasn't infinitive form, so "to can" is incorrect. It is therefore used "to be able to"