Can I still claim BCH from BTC core wallet after the 'BCH November 13' fork? I run a full BTC core node and use the bitcoin-qt core client wallet.

I have BTC in this wallet from before BCH was created. I have not yet attempted to claim my BCH.

After the upcoming bitcoin cash BCH November 13 hard fork upgrade activates, will I still be able to claim bitcoin cash (sweep or import from BCC to BCH wallet) from my bitcoin-qt (BTC) wallet?

I assume I can, but have not been able to find an explicit answer to this. I want to be certain I can claim BCH after Nov 13.
It depends on what exactly is changed in the upcoming hard fork, however the devs would not make previous outputs unspendable intentionally.  Your private keys corresponding to UTXO that you controlled at the time of the first fork should still control the same amount of BCH going forward.  If not, users would reject this upcoming fork.