Question: Should I keep my computer on to receive Bitcoins from other wallets?
You don’t need to keep your devices with Bitcoin wallets on while transactions are happening.
All transactions and Bitcoin Wallets are registered within the “Public Ledger” which is shared between all the devices on the network.
In case your device is off, once you launch your Bitcoin wallet, it will download blocks and record of transactions to keep you updated.
This way, Bitcoin transactions are always happening and recorded online publicly.