Why not べんきょうします?
That would mean "I will study". The word "studying" is in progressive tense (with the "-ing" ending), which uses the "-te" form of the verb.
勉強します also means "I study" in present tense. But yes, you are correct about the progressive tense.
I think it's the difference between "I study" and "I am studying".
can someone explain to me the use of "してい”
The dictionary form of study is "べんきょうする" you change that to "べんきょうして" and then you add "いる" after it (べんきょうしています) which basically makes it I am currently studying or I am studying.
Hope that helps
Why the "i" in the "imasu"?
Because Japanese uses the て-form of a verb + the ru-verb「いる」for the progressive tense, i.e.
why do we not use the を？
There is no object in this sentence to use を with. Literally, this translates to just "studying". The subject would be assumed based on the context.
You can use を: べんきょうをしています. It has the same meaning as べんきょうしています. In general, if the verb is noun+します, then it can as well be written as noun+を+します.