Product API questions

Product search API- is there a way to filter based on Category of products or Products available for a particular store?
Get Product API- I don't see following information in the response which would be very crucial when exporting this data to different system/external custom facing website:
- Product Shipping dimensions/weight etc
- Product Images
- Product description
Apart from these API endpoints do you have any API for following:
- fetch Pricing information of decoration added
- fetch global Color ids available