It's better to use past simple and also to qualify the amount of English you learnt in that sentence. 'I learnt some English today.' or 'I studied English today'. 'Some' is important because it's unlikely that you learnt the entire language in one day :) Past simple is better to use than present perfect here because you're referring to a completed action and part of a routine. Hope this helps!

Yes, if it's still the same day you say "I've learnt... today." If you give a time in the past, then you obviously use past simple: "I learnt... earlier this morning/after lunch/etc."