Suggestions for leg support and edge guard for countertop
The stuff for the green bit is edge banding. You can also use thin strips of the laminate that the counter is topped with if you can get it, or have some stashed, so that it matches better.

The usual approach to the blue bit is to simply put a sheet of plywood there, parallel to the washer/dryer beside it - or just put a cabinet there, rather than having an open hole. 

A cleat is screwed to both the countertop and the vertical plywood to make the joint.