Before washing (the first time only), put the hammam bathrobe in COLD water for about 12 hours (if possible, not necessary). This will make the fibers stronger and the absorption better. It also reduces shrinkage. Then wash it at 40 degrees.
Wash your bathrobe with similar colours. Hammam towels, and so the bathrobe, can be washed at 60 degrees and can be tumbled dry and being ironed.
You can clean the leather house slippers with a damp cloth and use shoe polish if necessary.