1. It depends. Could be more, could be less. At least in LN tx are only recorded as forwards in the forwarding peers, and the initiator and receiver of the transaction as payments. Blockchain is for eternity.
  2. No, L1 blockchains only require an unfunded address to receive payments.
  3. Equivalent, both require running a full node software. Bitcoin is negligibly more expensive to run given its older, larger chain.