I've never used Wasabi or CoinJoined before so I can't answer for that. For lightning, I've only used Eclair to send coins before (on my phone so I can't really give sound advice on that either.
Using Bitcoin Core offline :
- i have my bitcoin core wallet fully synced (bitcoin core 0.19.1), can i create an address while i am offline and after i have fully synced the wallet, if yes, then how there will be ever an coincidence that the offline generated wallet is already generated or will be future generated ? (I'm referring to the (How to Deposit Funds) in this article
https://en.bitcoin.it/wiki/How_to_set_up_a_secure_offline_savings_wallet)
No. Firstly, its a misconception that addresses must be made known to the network so that the rest can't generate it. It's completely untrue and it doesn't make sense (given Bitcoin's model). The generation of the address relies on the probability of someone else generating the same address as you. The probability is so small, that it would take you quite a few lifetimes even if everyone were to bruteforce it with the strongest computer today.
- lets assume i have a wallet with 1 btc, would bitcoin core after being fully synced and then go offline allow me to send 0.5 btc to address x and 0.5 btc to address y
and after the internet connection is back and i am online, the transaction would take place immediately as if it is just waiting to sense internet connection in order to log the transaction on the blockchain or not possible and i must send the funds while i am online
Bitcoin Core would send transactions only when it detects an internet connection and is connected to its peers.