With these fabrics, I'd wash the batik with all the reds, and the dark stripes and the other dark fabric. Everything else except the cream in another load, and the cream separately.
Vinegar will help set the colours, and a Shout Colour Catcher is another great product - throw it in the wash, it will gather up extra dye.
Cutting a corner off an edge will also help keep fraying in check.
I usually put in a bit of detergent, about half what I would put in a normal load - the fabric isn't dirty, but might be dusty from its journey to you. No fabric softener. When the fabric is damp-dry, press and starch. Then you're ready to cut!
LOVE the batik - your fabrics are gorgeous - what pattern are you making?