Q: Does this mean that the bitcoin addresses from computer1 are now active and able to receive future transactions on computer2?
Yes. And past transactions as well.
Q: Does importing the private keys automatically give me access to the public keys (i.e. the respective bitcoin addresses)
Yes.
or must I perform some other step?
No.
Q: When, if ever, will I need to enter the old passphrase from computer1 on computer2?
Never.
Will the imported keys simply need the multibit passphrase in order to spend?
Yes.
Thank you in advance!
You're welcome.
Note: MultiBit occasionally get out of sync with the blockchain. If you don't see the bitcoins that are associated with those addresses, you may need to reset the blockchain according to this into from the MultiBit website:
https://multibit.org/en/help/v0.5/help_support_sentBitcoinToMultibitButTheyNeverArrived.html
Quote
To get the missing transaction into your wallet:
1. Click on the wallet in the 'Wallets Wallets' side panel to make it the active wallet.
2. Go into the 'Tools | Reset Reset Blockchain and Transactions' menu option.
3. Select the "Specify reset date" and select the DAY BEFORE the transaction. (Lots of dates in Bitcoin are quoted in GMT so if you choose the day before you avoid time zone problems).
4. Click on the 'Reset Reset blockchain and transactions' button and let MultiBit sync the blockchain. Just leave MultiBit to work its way through the sync.
You should then see the transaction in your wallet.
1. Click on the wallet in the 'Wallets Wallets' side panel to make it the active wallet.
2. Go into the 'Tools | Reset Reset Blockchain and Transactions' menu option.
3. Select the "Specify reset date" and select the DAY BEFORE the transaction. (Lots of dates in Bitcoin are quoted in GMT so if you choose the day before you avoid time zone problems).
4. Click on the 'Reset Reset blockchain and transactions' button and let MultiBit sync the blockchain. Just leave MultiBit to work its way through the sync.
You should then see the transaction in your wallet.
