Can I forward an email based on content or sender (or whatever) but retain a copy in my inbox?
Yes. Email messages forwarded via filter will remain in you Inbox (unless you tell the filter to move the message).
First you need to set up and confirm a forwarding address. You do that under
Settings | Forwarding and POP/IMAP. Choose "Add a forwarding address". A confirmation code will be sent to the address you enter to ensure that you have control (or permission) to forward to that address. (This is an anti-spam measure.)
Once you have confirmed the forwarding address, simply create a filter as you normally would. (Usually with a search and then selecting "Create filter with this search".) Check the box that says "Forward it to:" and choose your forwarding address. Unless you also check "Skip the Inbox" any messages that match your filter will be forwarded to the address you've selected but nothing else will happen to the message.
More information from Google Support: Automatically forward emails to another account