How do I Reconcile Quicken with my bank statement, when the paper statement and quicken dates (and t

[All my comments here are based on matching the Quicken reconcile process with your "paper" once-a-month statement, even if you are looking at that "paper" statement online.]

• "Prior Balance 6,678.47 (when I started to do the Quicken Reconcile I put 0.00 in this box; later it populated to this figure."

The prior reconciled balance in Quicken is the total of all reconciled transactions for all dates for the account.  You should not need to change the value.  The value should agree with your bank statement for the "Starting Balance" or similar at the beginning of the period.  If the value does not agree, you should be trying to determine the discrepancy.  If you enter a different value that Quicken calculates, Quicken will create a transaction to make up the difference (not a generally good choice).  

• "Reviewed the paper bank statement with Quicken statement. The bank statement has at least 6 transactions totaling 1,1700.00 which these transactions don’t show up in Quicken."

Note Sherlock's comment was to look at the register (not the reconcile window listing).  If the transactions are not in the reconcile window listing, they may be in the register with a date after 2/7/19 or with a Clr status of "R" = reconciled.  If they are on your bank statement, they should not already be reconciled. Correct or keep as shown.  Already being reconciled would affect the starting balance then would not affect the final balance.  

Also note that the reconcile window listing should possibly go back to the beginning of the account listing all uncleared transactions through 2/7/19.  The 1/11/19 start date is immaterial.  You may have written and recorded a check in December that would be listed in the window as possibly clearing in January (or February or March...)