I know that one private key can generate more than one public key.
AFAIK, 1 private key only can generate 2 public key (compressed/uncompressed), but 1 public key can be used to generate multiple different type of Bitcoin address such as legacy compressed address, legacy uncompressed address and Bech32 SegWit address
My question here is, is it fine to save one of these public keys and use it as a receive address permanently? Will my ledger just create a new receive address each time funds are received that is usable for privacy reasons ?
There's no problem, even though re-use address have few security/privacy concern. But since Ledger Nano use HD (hierarchical deterministic) system, it only generates new address when last few address have activity.
P.S. I see unconfirmed transactions are quite low today, I can turn all my inputs into one input by sending my BTC to myself right ?
Actually, you can do it anytime, the only difference is confirmation time. But i suggest
not to re-use the address.