Ethereum to Layer 2 interactions: dYdX monitors the relevant Ethereum transactions, namely deposit, force withdrawal, and force trade. Upon receiving such transactions on Ethereum, the relevant operation (e.g., adding money to the user’s Layer 2 position), will take place on Layer 2.

Layer 2 to Ethereum interactions: After a batch of transactions is executed off-chain, the proof to its validity is generated and verified by a STARK verifier on-chain. After the STARK verifier approved the state transitions, it takes effect, including changing Ethereum balances of users due to deposits to or withdrawal from Layer 2.

At first, no. However, as more and more Layer 2 rollups emerge, StarkWare understands the importance of supporting this, and adding this feature is certainly on the roadmap.

If adoption becomes fragmented across a number of different rollups in addition to liquidity on Layer 1 vs Layer 2, Ethereum's base layer is likely to lose some composability, at least in the short term.

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