You have clearly asked your doubts in point form. It makes it easier for us to answer each point.
Is this going to be a long term relationship or are you in it, just for the sex. Reason I ask, is because you have doubts whether your girlfriend is a virgin? Not a good way to begin a relationship with doubts about her virginity.
1) You must believe and proceed that she is a virgin. Yes, sex for the first time for a girl is a bit painful, but she soon gets over the pain and begins to enjoy the sex act the second time around. If the hymen is intact (if it is not, it does not mean that she is not a virgin, as the hymen can be broken in other ways like exercise, use of sanitary pads, cycling etc), then when it is broken, either due to your penetration of her vagina either with finger or penis, there will be some bleeding and some pain.
2) It is always best to use a condom. Read the questions here, of Users who go through hell, when they have not used a condom and fear about their partner getting pregnant. You can avoid all that tension, by using a condom in the proper manner. Be smart and educated about the risks you take when you do not use a condom. Sex may be a little less pleasurable for you, but the safety is worth it. You also have doubts whether your girlfriend is a virgin or whether she has had other sexual partners. The best way for you to avoid contracting any STDs is by using a condom.
3) There is no other way.
4) Pills are an emergency contraceptive and not meant to replace the condom. There are many side effects and her menstrual cycle will go for a toss. This will add to your tension. She will keep screaming, I am pregnant and you can imagine what this will mean for your peace of mind.
Enjoy yourself but act wisely.