# Proving decidability and undecidablity of CFL DCFL problems [closed]

I am trying to understand how can I prove various problems of CFLs and DCFLs are undecidable or undecidable.

For context free grammars $$G, G_1, G_2$$, how can I prove following problems are undecidable:

1. Whether $$L(G)$$ is a regular language?
2. Whether $$L(G)$$ is a DCFL?
3. Whether $$L(G)^c$$ is CFL?
4. Whether $$L(G_1)\cap L(G_2)$$ is CFL?

For deterministic context free grammar $$D$$ and regular grammar $$R$$, how can I prove following problems are decidable:

1. Whether $$L(D)\subseteq L(R)$$
2. Whether $$L(D)=L(R)$$
3. Whether $$L(R)\subseteq L(D)$$

I gave following attempts:

1. I know whether $$L(G)=\Sigma^*$$ is undecidable. $$\Sigma^*$$ is regular language. So, problem 1 is undecidable.
2. Undecidability of this problem follows from undecidability of 1st problem, since set of regular languages is proper subset of set of DCFLs.
3. I am unable to come up with any logic for this.
4. Given that I know whether $$L(G_1)\cap L(G_2)=\emptyset$$ is undecidable. $$\emptyset$$ is CFL. So, problem 4 is undecidable.
5. Given that I know, $$L(G)\subset L(R)$$ is decidable, $$L(D)\subset L(R)$$ is also decidable as set of DCFLs are proper subset of set of CFLs.
6. Decidability of this problem follows from 5th problem.
7. I am unable to come up with any logic for this.

Was I correct with my attempt? Also can someone help me out for problem 3 and 7?