If my Quickbooks is already connected to my bank account, do I still need to manually enter the checks I've written, and do I also need to enter my deposits as well?

YES!  And if we're talking "best practices" your Credit Card charges too!

The Bank Feed really should not be used to replace good bookkeeping and know what you've written checks for, charged on your Credit Card or even made Deposits.  The purpose of the Bank Feed is to show you what has hit your bank so in most cases you can quickly match those transactions to what you've entered.  And if there are transactions are not yours or there are discrepancies (reversed numbers, etc.) those few items will stand out and can easily be resolved. 

Some of the biggest horror stories I've heard about are when people go for months just accepting and entering transactions from the Bank Feed, then figuring out there is a major issue.  Often it's money to have the Accountant clean things up at Tax time OR there was money going out of the company and it just wasn't caught.