Note to asker: questions are answered in brief. I think you are asking too much by placing 3 questions in one, each of which commands an essay-style answer.
For future reference, just ask one question, and reduce it to just what component of the question you don't understand.
I am assuming you understand the originate-and-hold business model of banks.
Having a 30-yr fixed rate mortgage, which is funded by short-term retail deposits (although your short-term is not exactly defined) exposes the bank to the following:
a. interest rate risk - duration of the mortgages (Google: Macaulay duration) is much, much longer than the liabilities; duration GAP is large. Maturities of the assets shorter than the maturity of liabilities - bank is "short-funded".
In mismatching of the maturities and liquidities between assets and liabilities, the bank exposes itself to interest rate risk.
if market rate of interest increases, could potentially have Net Interest Margin (interest income from assets less interest expense to liabilities) decrease, or even yield negative.
b. insolvency risk - this could arise from the interest rate risk, and from unexpected deposit drains. This could lead to the bank having to liquidate all of its assets (if drains extend beyond its "economic capital"). Once bank has reached stage where it still has not met the demand of depositors, and cannot get more liquidity (i.e. by fire sale or by bought-in liquidity), the bank is unable to meet need of liabilities >>> insolvent.
c. regulatory costs - holding assets to maturity can cost the bank expensive capital, and holding illiquid assets to maturity can constrain the bank's growth.
benefits: reduces interest rate risk and liquidity risk (and other residual risk from these two).
costs: net interest income would be reduced. not a good thing, as this reduces profitability of bank. also, may be difficult to attract funding if bank only issues long-term deposits, unless interest rates are very high - again reducing revenue.
why not originate only adjustable rate mortgages that match maturity/duration of liabilites:
a - liabilities to match duration of mortgages would be unrealistic. who is willing to tie their cash in for 30 years?
b - equally, mortgages to match duration of liabilities would also be unrealistic. lending a huge amount for short term will mean you will have to demand a higher interest rate. also, credit risk would be exacerbated as probability of default increases with interest.
what is MBS?
the collection of mortgages, repackaging, and sale. turning illiquid assets into liquid, tradeable assets that offer attractive returns to investors.
- benefits to bank: a) reduces capital required, b) reduces credit, interest and liquidity risk, c) new source of funding; if credit ratings of MBSs is higher than the bank's own rating, then this would be a cheaper source of funds for bank, d) enables bank to diversify its portfolio and reduce risks.
costs to bank a) costs of insurance and guarantees for MBSs, b) valuation and packaging costs
benefits to investors a) enables diversification (MBSs are divesified enough to suit risk preference of different types of investors, b) yields superior returns as compared to other secutities that are comparable in terms of maturities and risk.
J Bessis - Risk Management in Banking (3rd edition)
A Saunders & M Cornett - Financial Institution Management - A Risk Management Approach (6th edition)