You are going to building a series of joists that presumably terminal at rim joists and then shim this floor assembly level. Are you putting plywood on top of it so that your tiles sit on the plywood?

If you make a 12'x14' floor assembly out of 2x2 joists with rim joists and this is for the most part sitting on the ground, you could shim with composite shim or make your own from decking offcuts. Another option is you could use a non-shrink structural grout in any space between the joist and the slab and use get a mortar bag to apply it. If the heave in the slab is making the assembly not level chip/grind it out.

You are going to building a series of joists that presumably terminal at rim joists and then shim this floor assembly level. Are you putting plywood on top of it so that your tiles sit on the plywood?

If you make a 12'x 14' floor assembly out of 2x2 joists with rim joists and this is for the most part sitting on the ground, you could shim with composite shim or make your own from decking offcuts. Another option is you could use a non-shrink structural grout in any space between the joist and the slab and use get a mortar bag to apply it. If the heave in the slab is making the assembly not level chip/grind it out.

Your deck is covered, the concrete base is porous, assuming water is not pooling under the deck in a storm I don't think you have to worry too much about drainage. If the water has previous pooled on the concrete then you might want to worry more about it.

To keep the shims in place you could either use the grout or use an adhesive (PL Premium). Direct contact between the PT 2x2 and the concrete is fine assuming there is no puddling of water.

You are going to building a series of joists that presumably terminal at rim joists and then shim this floor assembly level. Are you putting plywood on top of it so that your tiles sit on the plywood?

Why not just go with composite board decking and make a proper deck on top of your 2x2 floor assembly?

You are going to building a series of joists that presumably terminal at rim joists and then shim this floor assembly level. Are you putting plywood on top of it so that your tiles sit on the plywood?

If you make a 12'x14' floor assembly out of 2x2 joists with rim joists and this is for the most part sitting on the ground, you could shim with composite shim or make your own from decking offcuts. Another option is you could use a non-shrink structural grout in any space between the joist and the slab and use get a mortar bag to apply it. If the heave in the slab is making the assembly not level chip/grind it out.