Im 20 weeks pregnant this weekend and due on the 14th April, my charts say that I conceived on July 22nd I slept with someone on the 18th and the 20th is it likely that the first encounter on the 18th is the father or is that to long for the sperm to last. Im hoping the father is the second male on the 20th as that is my boyfriend and he's very excited to be a father please help.!

IMPOSSIBLE to tell as the dates are too close.
Dating is all Best Guess and if there is a doubt over paternity then a DNA test will need to be conducted AFTER the birth.

When you work out how far along you are in pregnancy e.g. I am 20 weeks do I count back 20 weeks to when I conceived or is it actually 18 weeks and the doctors add 2 weeks?

Will depend on how the doctors determine the date, depending on the info given by you.

Most often it is figured form Last Period.

But there is no way to know an exact conception date, even at best it is give or take one week, often give or take two weeks.

Sorry, conception dates, are estimates and at best are give and take one week.

There is no way to even be sure what week it happened, and no way at all to know an exact day.

So this close it is not possible to know. You will have to get a DNA test to know the father