The best way to sort out the home button problem is to first turn your phone off and preferably have it in a case. Then get a damp cloth and rub it over the home button rather vigorously in every direction and then around the edge of the button(inside edge) again fairly vigorously. Then turn the phone over and tap it quite hard on its face(hence the reason why a case is best) about 5-10 times. Then turn it back over and dry the phone thoroughly. This should sort it out.
When I did my 6 it completely sorted the problem out. I also did it with my 6s as soon as I got it and my Air 2. When I did mine I put the phone in an apple leather case and when I was tapping it I did it on my Air 2 Smart Cover.