Some crypto shows Node not in Sync

This means you cannot Deposit and Withdrawal crypto from/to any other exchange.

Sometimes you can only deposit the coin but withdrawal is disabled then also it shows Node Not in SYNC and vice versa.

Can I able to trade (buy and sell)?

Yes, you can trade the token by just going to the Trade page of that particular coin but after buying you will not be able to withdraw if Node is not in Sync.