I had a medical abortion on April 10th due to medical reasons. It has been exactly 1 month and 2 days and I still have not started my period. I was told by the doctors I could start having intercourse after 2 weeks. I had unprotected sex on the 27th April, 2nd may, 3rd may and the 9th may. Is it possible for me to be pregnant again right after an abortion and if I was having intercourse on those dates. I took a pregnancy test last week and it came out a really faint positive line, quite hard to see. Im guessing this is from my previous pregnancy as I have read that pregnancy hormones can still be present after an abortion.

Your hormones are still on 'pregnancy mode'; probably why you tested positive.
But who can say, get checked out by your doctor.

After an abortion, medical or otherwise, I would not want to take a chance of becoming pregnant again for a long while, until everything settles down.

Its going to be 5 weeks on the 15th that I have not started my period. Do you no how long it takes for a period to come back and after how long I should take a pregnancy test as I thought I should have had my period by now.

There is no set date. It varies widely. I too would not be trying to get pregnant so soon.
You say your abortion was for 'medical' reasons but not what they were.
You certainly don't have to say, but it makes it difficult to answer questions.
Therefore these are questions for your doctor.