I'll answer your question #3 - banks/institutions primarily sell their loans in order to free up capital and reduce interest rate risk.
For example, if you take out a $100,000 loan, somebody somewhere is actually coughing up $100,000 cash to give to you. If it's a bank, that means (generally) that enough people have deposited $100,000 in that bank to come up with enough cash to lend you the $100,000. The bank charges you, say, 6% on the loan and pays their depositer 2% interest on their savings account. The bank keeps the 4% spread as a difference. In the meantime, while holding your loan, the bank runs the risk that you will repay that loan early (either because you sold the house and simply paid off the mortgage or you refinanced somewhere else).
If they instead sell your loan right away, they get the profit from the sale of the loan and have the $100,000 back in their account. Granted, now they need to invest it somewhere else to pay their depositers 2%, but they have eliminated the risk that their income stream (your monthly interest payments) have stopped.
In addition, by holding your loan, they need a servicing department to handle your monthly payments, etc.
Alot of Credit Unions and local S & L's do hold and service their own mortgages. That's why they also tend to pay the highest interest rate on deposits. If you watch closely, you'll notice that their mortgage rates also do not fluctuate as much as mortgage brokers or other institutions that sell their loans; that's because they need to be concerned about getting too many low interest rates on their books (because it that happens, and interest rates start to rise, then they are forced to pay out higher rates to retain depositers, but are stuck collecting interest payments on low rate loans).
Note that mortgage rates tend to follow the ten year Treasury Rate. That's why mortgage rates went up last week when the Fed cut the rate.
