No you can not delete entries, it will change the balance as well as the income statement (P&L)

If you did a balance adjustment it will show in the balance adjustment account (chart of accounts) and on the P&L (an expense). A small amount will work but if it is fairly large you need to work things out, a balance adjustment account listed on your income tax filing is like holding up a sign saying " I have no idea how to do this" to the IRS.

Yes unreconciled entries means there is an outstanding check which lowers your bank balance, if your balance is negative that is an important issue