The brownish stuff is most likely diatoms, very common in new tanks. It should disappear as the tank matures. The green algae may also cure itself. If you still have it in a couple months there may be other issues to address but I wouldn’t worry until then.
Stripes and spots are normal for a healthy ghost shrimp. As for the missing legs, couple of molts and they should be OK. Hard water is actually beneficial for most invertebrates. If your water is extremely hard you can cut it with distilled water, but don’t use distilled water exclusively.
See if there is a landscaping supply place nearby. They usually sell things like gravel by the cubic yard for driveways but many carry multiple types of stone as well. Most are willing to sell smaller amounts for very cheap.