If you decide to host your ASIC, make sure to check what feature/service they offer. Small provider is less likely to offer repair service or handle RMA on your behalf.
Oh that shouldn't be a issue but yes your right no doubt certain histers receive kickbacks from mining pools
You can't mine without a mining pool, the time people used BitcoinCore to mine is long dead ago. Even solo miners point their hashrate to solo pools
To be more specific, solo miner usually choose solo pool (rather than running full node software) due to these reason,
1. Faster block propagation, which reduce chance of your mined block become stale block.
2. Don't have to download and optionally store ~500GB of blockchain.