My boyfriend doesnt trust me, what do i do Options

[*Weird addiction*]

ok this is kinda long

ive been with jeremy for like a month....i was with him at the mall and i saw him kissing his ex and i got mad and confronted him and he told me that he still has feelings for her...then i told him never to do it again and he said "ill kiss whomever i want" and i said "in that case why dont we break up" and hes like..."no, ur in love with 'tim' and i still have feelings for kayla (his ex) so we're even" and im like "i dont love tim,hes just a guy i met in xanga,and he's in the states and im in belgium,"wow that's far....and he's like " dont lie to me,ive read the messages u sent to him,ur email...ur telephone conversations, u talk about him alot"...jezus,tim is just a friend,i dont like him...he's been spying on me! my friend told me that one day he called to confirm if i was really at her place cos he wasnt sure,i asked him and he denied it, how did he get my password???...i dont know what to do...should i dump or stay with him?? besides tim and i dont communicate much again...what kind of a bf is that??