This shit can happen.
How can this shit happen by mistake? You can't just "find out there's a timelock", you need to consciously specify it.
How do you mean. I have an address to which people send money. I see money come in from my wallet, but at that moment i don't know if a timelock is on it, do I?
If the wallet generate P2PK, P2PKH or P2WPKH address i can be 100% sure there's no timelock or other custom condition to spend it. On top of that, there are almost no Bitcoin wallet which support timelock feature.
I don't think so. Electrum wallet has a feature that places a timelock.