That bird has male specific feathering. Those long, thin feathers near the base of the tail are male saddle feathers. Someone else in your coop is laying the eggs. They aren't coming from 'Susan.'
Yes. They need a heat source to keep them warm until their feathers are all grown in. Gradually raise it a bit every couple of days. At the end of 4-5 weeks, they should be able to tolerate 70-75 degrees with no problems.
x2 Scrambled eggs make an excellent substitute for young chicks until you can get them some starter. If you don't get medicated starter, make sure you have some Corid or other medication for coccidia, just in case.