can you send to NXT to a wallet with only public key

if I only had the public key of an address, could funds / currency be sent there?
i.e. you do not know the wallet address, but have the public key, can the public key be used to send address to its wallet?

I am not sure. I don't suppose its relevant because one could just as well use the address.

I am just curious if persons could gain less information if they shared only their public key - would this prevent people from seeing their wallet address and its balance? Sorry if it is not a relevant question. I am not sure if I have conveyed my meaning properly.

The account id (as a number) or the RS format are equivalent: both are just representations of an unsigned 64 bit integer. The public key is 256 bit long and the 64 bits account number/address is easily computed from the full public key.

About your specific question: yes, in a sense you can send directly to the public key. As from the public key you can easily derive the account id both are somehow equivalent. The only practical difference is before the first transaction sent by the account. More information: Ardor Frequently Asked Questions

You can use this API call to get the account id and RS encoded address from a public key. To go the other way around (from account id or RS address) you can use the getAccount API call.