Last year applications per place for Mech Eng was 5.9:1, Eng generally is competitive at Imperial but as long as you've got a solid academic record, a good personal statement and a good reference from your school I'm sure it would be no trouble getting an interview.
I don't know much about how much importance the Mech Eng Dept. places on interviews, but usually an interview means you will be offered a place.
And yeah, Mech Eng requires 3As (check the prospectus), maths and physics are compulsory. FM is certainly favourable I'd think, since the first year of Engineering degrees usually contain a lot of maths covered in FM.
Can't really tell whether you'd struggle on the course, I don't study it! If you meet the offer for the course then that means you're bright enough to do it I'd guess.