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When Einstein first proposed GR.. did he mean it to have fixed curved background or dynamical?

2. As I understand it. At present. We treat GR as fixed curved background.. so that when we do QFT in curved spacetime, we fix the stress-energy tensor everywhere so that we have a well-defined solution to the EFE, and that fixes the spacetime geometry everywhere. But is this how it should be done.

3. What would happen if you don't fix the stress-energy tensor everywhere but it is dynamical.. can't you do any QFT this way. Is one of the purpose of String theory to make the string planck size so that you don't have to deal with this problem of dynamical stress-energy tensor.. or do Strings able to somehow still have well defined solution to the EFE in spite of the stress-energy tensor not fixed everywhere.. how does it do that?

4. What other quantum gravity theories able to have well defined solution to the EFE in spite of the stress-energy tensor not fixed everywhere.. how does that particular QG theory do that?

5. And is this problem about dynamic background and still having well defined soluton the EFE exactly the purpose of quantum gravity?

I'm not sure of most sentences above.. so please emphasize whether the answer is yes or no to the 5 questions. thanks!