To answer your first question; yes, at your age you can impregnate a woman. Men in their 90s have been known to father children.
As for your relationship with your girlfriend; stop playing around with possible dates of conception and tell her you will demand a DNA test as soon as the child is born (if the child comes to term) and if the child is not yours; your girlfriend is out of your apartment and out of your life. Unless of course you don't have a problem with her being sexually promiscuous and possibly infecting you with an STD she picked up from someone else. She's obviously not practicing safe sex.

