I don't think it is necessary to write the ":00" when adding am.

I would write 10am, without space...

10 a.m., 10 A.M., 10 am, 10 AM can all be right depending on the house style.

10am without a space is wrong.

10:00 a.m. is indeed unnecessary.

Conventions vary regarding whether :00 is needed following an hour. There should always be a space between the last number and am or pm (just as there should be one prior to a unit of measurement, e.g. 250 g, not *250g)