I just created my first lightning node and already have one active connection. My problem is however, that I do not see my node in any lightning network explorer. Is it possible to somehow check whether my node is truly online/visible?
For your node to appear in one of the explorers you have to have at least one open channel and once the channel is open you have to wait a little bit since the information that your node exist has to propagate through the gossip protocol. The gossip protocol requires an active channel to prevent spam and denial of service attacks.
To check if your node is online you can however peer to any node. (in clightning with the command lightning-cli connect) if that command is successful your node is online.