You're welcome!
(I changed the order of your questions to make my explanation simpler.)
Consolidation is useful for simplifying your finances, since it's easier to track and pay a single loan. Consolidating through the government's program could actually end up costing you a little extra money: since you round up the weighted average interest rate to the nearest 0.125%, you may end up paying a little more interest in the long run.
The financial advantages come when you refinance. With refinancing, a new lender pays off some or all of your loans, then issues you a new loan with its own terms. Generally, they'll present you with several repayment term/interest rate combinations from which to choose. Remember what I said about longer terms equaling higher interest rates (because with a longer term, you're tying up the lender's money for a longer period). You can select a more aggressive repayment term, which will lower your interest rate and the total amount of interest you pay over the life of the loan, but does so at the expense of higher monthly payments. Or you can choose a longer term and a lower monthly payment, understanding that the higher interest rate means you'll actually pay a bit more in the long run. You don't get somethin' for nothin'.
The government's program only allows you to consolidate, and you can only combine federal loans. Private lenders will allow you to consolidate and refinance, and they'll allow you to combine federal and private loans.
When you consolidate through the government's program, you're combining direct federal loans, which all compound at the same interval. If you consolidate/refinance with a private lender, generally you'll be in repayment with monthly compounding right from the start.