which tense they are used when they said

gelem

gelen

Gelem mi?

Have a look Here

Geleyim: let me come. 

And for gelen: ıt means the coming, so it´s not a form of any tense. 

-en-an is a suffix that is added to the stem verb that describes the one doing the action resulting in an adjective. 

Here´s a link for Gelen: http://www.turkishclass.com/forumTitle_57709

Gelem must be a typo: http://tureng.com/search/gelem

"gelem" is actually same as "geleyim" [let me come] this is used in some regional dialects in Anatolia. Some examples :

Bugün sana  gelem  mi ? . ---> Shall I come to you today ?

Oraya nasıl gelem ? ---> How shall I come there ?

more examples :

Gidem 

Görem

İçem

---------------------------

gelen ---> the one who comes /came

Buraya gelen herkese söyle ---> Tell everyone who comes here.

Bugün gelen adamı tanıyor musun ? ---> Do you know the man who came today?

Very Clear, Thanks for all.