he can't "evict you", so don't worry.
he must serve you with the proper documentation, which by the sounds of it, he doesn't have a clue about, so try not to stress.
tell your FIL to tell LL to get in touch with YOU/your DP, in WRITING, stating what rent, he thinks has not been paid, and the dates in question.
You can then reply with evidence that it has, in fact been paid.
he can't chuck you out by passing on a message via you FIL.
IF you are indeed 2 months or more behind in rent, he must serve you with a section 8 notice, and then apply to the court for a possession order, if you don't leave, which he can't force you to do.
IF you're not behind with the rent he can issue a "no fault" section 21 notice, but he must give you at least 2 months notice and this must run in line with your lease. Anything wrong in terms of dates etc will render it invalid.
Did you pay a deposit, and if so, is it protected?
Pop over to the money saving expert housing forum, they will be able to help.