I don't think you can have incoming connections over tor, only outgoing connections.
You don't need to open port 8333. You only need it if you want incoming connections, which is not necessary. You only need outgoing connections for it to work.
You can have both. There's quite a few nodes setup over tor for users to use.
Yes. Without opening port 8333, you can relay blocks and transactions around your eight onnected peers. However, it isn't helping too much by running full node, you are allowing more users to connect to your node and synchronize from it.