could I do the following offline [...] and when bitcoin core is online,
- the transaction gets broadcasted to the network/blockchain and eventually you will get the 0.1 btc I have sent you
Yes, your transaction will be broadcast once Bitcoin Core has been fully synchronised with the network after you go online. You can always sign a transaction in Bitcoin Core and broadcast it using third-party software if you need to spend your funds urgently (assuming you didn't receive any more coins).