Custardo "get her on the pill"?
Are you for real? What is she, a dog that needs to be spayed or something for her own good?
OP, definitely sit down and have a talk with her, you have no idea what she's been up to but it's not unreasonable that she's at the point where she needs to know where to turn, what her options are, etc. Explain that you had her at 16 and you know what being a teenager is like (she won't let on she believes you, but it will stick, trust me) and you understand that she's growing up and you want to help her make the right decisions and be in control of her life as she becomes more independent.
If she wants birth control, fine. If she wants reassurance that she can say NO to anything she doesn't want to do, that's fine too. Let her know you're there to talk to, or point her in the direction where she can get advice or help without you too.
With regard to boyfriends in the house, again, a frank discussion. Say you need to discuss this with your DP before you decide, and that the world won't end if the BF isn't allowed to come over tomorrow.
Once you've discussed and compromised with your DP on what the boundaries will be, then let your DD know and be firm but reasonable about it.
Lastly, get to know this boy, invite him over lots when you and your family are home, give him every chance to impress and earn your trust.