The Axiom of Dependent Choice (DC) is often considered to be an "intuitive and non-controversial" version of choice used in the proofs of many theorems in Analysis. Similarly, the Axiom of Determinacy (AD) leads to especially nice properties for real numbers. Thus, in a sense, the system ZF + DC + AD is much "nicer" than ZFC, but maybe it restricts the "richness" of the set theoretic universe in some ways. Hence, I am wondering how this system interacts with large cardinals.

In particular:

1. Since AD is inconsistent with unrestricted Axiom of Choice (AC), are any of the "standard" large cardinal axioms - strongly inaccessible, mahlo, measurable, rank-into-rank etc - inconsistent with ZF + DC + AD  ?
2. Conversely, can any such large cardinals - for example, strong inaccessibles - be proved to exist in this system  ? (Since the usual objection to proving their existence doesn't exist in this system)
3. Will the typical "size relations" between large cardinals in ZFC hold  ? For instance, is a measurable cardinal going to be inaccessible in this system  ? (The only proof I know uses well ordering) Is the smallest measurable greater than the smallest inaccessible  ?

I realize the question is quite broad - I am interested in sampling the kinds of results that may have been proved/conjectured.

The Axiom of Dependent Choice (DC) is often considered to be an "intuitive and non-controversial" version of choice used in the proofs of many theorems in Analysis. Similarly, the Axiom of Determinacy (AD) leads to especially nice properties for real numbers. Thus, in a sense, the system ZF + DC + AD is much "nicer" than ZFC, but maybe it restricts the "richness" of the set theoretic universe in some ways. Hence, I am wondering how this system interacts with large cardinals.

In particular:

1. Since AD is inconsistent with unrestricted Axiom of Choice (AC), are any of the "standard" large cardinal axioms - strongly inaccessible, Mahlo, measurable, rank-into-rank etc - inconsistent with ZF + DC + AD?
2. Conversely, can any such large cardinals - for example, strong inaccessibles - be proved to exist in this system? (Since the usual objection to proving their existence doesn't exist in this system)
3. Will the typical "size relations" between large cardinals in ZFC hold? For instance, is a measurable cardinal going to be inaccessible in this system? (The only proof I know uses well ordering) Is the smallest measurable greater than the smallest inaccessible?

I realize the question is quite broad - I am interested in sampling the kinds of results that may have been proved/conjectured.