I've got a bitcoin-qt wallet on computer1 with some bitcoins.
The wallet is encrypted with a passphrase.
I also have a multibit wallet on computer2 with some bitcoins.
Multibit on computer2 has a different passphrase from bitcoin-qt on computer1
If I export my private keys from bitcoin-qt on computer1 and
if I import those private keys into multibit on computer2,
Q: Does this mean that the bitcoin addresses from computer1 are now active and able to receive future transactions on computer2?
Q: Does importing the private keys automatically give me access to the public keys (i.e. the respective bitcoin addresses) or must I perform some other step?
Q: When, if ever, will I need to enter the old passphrase from computer1 on computer2? Will the imported keys simply need the multibit passphrase in order to spend?
(I don't want to simply transfer the bitcoins from bitcoin-qt to the addresses on computer2 because I don't want to wait to download the entire blockchain since last accessing the wallet on computer1)
Thank you in advance!