If I use diamonds to buy extra land do I lose the stars and compasses I've collected?

When you use diamonds to speed up land availability, you are essentially paying for the compasses you are lacking. For example, if you already have 10 out of 40, then the diamonds are paying for 30 compasses. Then the next plot of land will start at 0 compasses out of 40.

There is no affect on stars. Stars are a marker of your progress in the game and will never go down in number. You receive the stars as you fill them up in the course of playing the regular hidden object scenes, 5 stars max per scene (=25 stars max per chapter).