Can you show meProfessional red 2 1/8” tees only.

A little less that 1/2 inch-Standard

Can they be used with a golf mat that accepts wooden tees or are they too short? My concern is that they will end up level with the hitting surface

I use these on the mats at our city run par 3 course. They are decent mats and I Only use these 1-1/2" tees on the 4 longest holes. On the one Par 4 hole on the course, 276 yds, it sits the ball up high enough for using my 3 wood just fine ( for me anyway ) - approx 1/2 to 3/4 inch

Are you supposed to push these in the ground to the top of the color band?

If you're asking if the color band is some sort of guide as to how far the tee is supposed to go in the ground, it's not. Put the tee in the ground as far as you want. This company offers tees of different lengths; each one with a different color band. If you have a bunch of different length tees in your bag, the color band allows you to easily identify the length tee you're looking for.