Do not dump him over this he may have gotten it from a previous relationship or you may have gotten it from a previous relationship. I just found out I have it and I'm pregnant the nurse told me that this is nothing to ruin a relationship over especially if its a good relationship. If you had sex with him(oral, anal or vaginal) you most likely have it. Don't worry it's curable. And really if you don't expect him to be cheating just leave that alone and get checked asap because it can cause infertility and blindness to a baby.
Almost certainly, but you may not be showing any symptoms.
If you have had sexual contact with him then yes it is very highly likely he has given you it... You also need to ask yourself why he caught it if he's meant to be going out with you... Dump the dirty beast!!