Can I send/receive nano if my node has not fully synced yet?

Can I make transactions while my node is not 100% in sync with the network?

It’s possible as long as your account has been bootstrapped. When that happen is unfortunately a bit luck based right now in v19 and the “local account priority bootstrapping” item that has been planned for a while has been moved into the research section with unknown feature target. Updates related to this are targeted for V20: better prioritization of bootstrap accounts using a pre-calculated list of high depth accounts.

More info here