We give funds to employees at the beginning of the week to pay for expenses incurred during the week. They in-turn return any balances if any at the end of the week with receipts of all expenses.

We debited Employee i.e. Birenda Adv 3000
Credited Cash 3000

Then recorded each expenses as a debit i.e. Expense 1- 991.63
Expense 2 -991.63
Expense 3 -991.63
Birenda Adv 2,974.90

Birenda had a bal of 25.10
So we recorded that as Cash 25.10
Returned Adv 25.10

Our accounts add up to 6000...

Are we recording correctly?

You've got the idea but easier just to do one entry:
Dr. Expense 1 991.63
Dr. Expense 2 991.63
Dr. Expense 3 991.63
Dr. Cash 25.11
Cr. Advance 3000

You can't credit "returned advance" because that wasn't the account name. Use the account name, not a description of what happened.