Batching state-dependent transactions to RPC

[EthanBlockson]

I've done a lot of research around it, but still clueless:

1. Are public RPCs able to receive batched state-dependent* txs in any EVM, like Flashbots do?
2. Does running your own node give any additional capabilities to perform this kind of batch from question 1)?
3. Is a bundle-or-fail scenario ever possible while sending a batch of state-dependent* txs to public RPCs/from your own node?

*By state-dependent txs, I mean those strictly dependent on each other, like first step: to prefill empty address with ETH for gas, and second step: to call something from it.

@ricmoo I'd be grateful for your pick on this