Washing machine: Yes. Polyester can in most cases can be machine washed. Hot temperatures should be avoided, though. Go for warm temperatures around 40°C (100 °F).
Hand wash: Yes
Mixed wash: Yes. Polyester doesn't mix with the dye from other fabrics.
Dryer: No. The intense heat can damage the fabric as well as zipper pulls, straps, etc. Polyester is a quick-drying fabric, so just hanging it up will do the trick.
Bleach: No. Bleach can cause miscoloring and damage to the fabric.
Hot water: No. The high heat can cause the fabric to break down and lose its color. Warm water, on the other hand, will not harm the material and is more effective against stains in comparison to cold water.
Detergent: Yes. Average or mild detergent won't harm the fabric. Strong detergent should be avoided.
(In this picture: Thule Exeo backpack)