‘Besides’ means ‘as well as’, ‘in addition to’ :
‘Besides English, she is (also) learning Japanese’.
You don’t need to include the word ‘also’.
‘Also’, too, can mean ‘as well as’ :
‘She is also learning Japanese’, but note that you haven’t included a reference to English. This is understood from the conversation.
‘Besides A . . B’ : you state both the references.
‘also B’ or ‘B also’ [without stating A] : A is already known from the previous conversation.
The word ‘too’ can also be used to mean ‘also’, but can only be placed in certain positions in the sentence :
‘She is learning Japanese too’ i.e. ‘she is learning Japanese also’ ; however you can’t say ‘she is too learning Japanese’.