1. Can the Rook Post Mount work with vinyl post sleeves manufactured from different companies?

Yes, it can be used by 4 inch x 4 inch and 5 inch x 5 inch vinyl sleeve with a wall thickness of .165 and thinner.

Rooks will not work with 4 3/4 x 4 3/4 which is commonly sold at the big box stores. (Lowes and Home Depot)