According to the information . . . if the car was registered as new on 1 February 2015, then the first MOT will have to be done NOT LATER than 1 February 2018.
Yes, indeed.
My car had its first MOT this year. It had to be done by 24/06/18 and I had it done on 04/06/18. The next one is due by 24/06/19 and the earliest it can be done is 25/05/19
you can take your car in within 28 days of its 3rd birthday and have the MoT valid until its 4th birthday. ie, it works like subsequent MoTs in that, so long as you are within 1 month of an MoT expiring your new one is valid for 1 year after the expiry of the old one.