No, No and No. A FTO will throw anyones CV in the bin regardless of age. Best to do your instructors course where you would preferably would like to fly as quite often you will be offered a job on completion of your training. I got my FI(R) when I was 35, fellow instructors at my FTO got theres in there 40's no reason why it should not be 50's or 60's. In fact this is probably encouraged as older instructors are less likely to move on to airline jobs and promotes stability within the school.
have a nice day
MJR