No, nodes don't need to run 24/7. For a while I've been running some nodes only at night and during the weekends, when electricity was cheaper.
What happens if I do some transactions, the switch it off and switch on in a few days?
Your wallet will still have your private keys, ready to sign transactions to expend your utxos. The node will synchronize the blockchain when you turn it back on. If it's been just a few days off, synchronization won't take too long.
What I usually do is having small amounts on LN or on-chain wallets on my phones ready for quick small transactions while my nodes are off.
I'm glad I could help. It's all a little confusing at first, although not complicated.
Perhaps you could start running a testnet Bitcoin node. Synchronization takes much shorter, disk space is much less, and stress for the possibility of making a mistake is also reduced a lot.
Also, it's cool helping run the testnet and you can try any crazy thing you might think about. :-)
Totally noob question: Does the node really have to run 24/7? What happens if I do some transactions, the switch it off and switch on in a few days?
I will still be able to do more transactions but only after it has synched the blockchain?