is when the central bank purchases investment maturity bonds in return for bank reserves and involves no change in the net financial assets of the non-government sector.
is when the central bank floods the banks with new money (new net financial assets) to encourage them to lend in order to ease the credit crunch
involves the central bank printing new money and is thus the same as government spending which is not financed by debt

if taxation revenue falls in a recession and the government wants to introduce a stimulus package.
if the central bank desires to maintain a constant short-term target interest rate and net government spending is rising. (note comments)
to finance the budget deficit if the government is worried about "money creation".

put downward pressure on short-term interest rates because they increase bank reserves in aggregate which then stimulate competition in the Interbank market.
put upward pressure on interest rates because the government is competing for scarce savings that could be invested elsewhere.
have no implications for interest rates because the ratings agencies basically set the risk rating of public debt.

allow the Federal government to build sovereign funds which then help it solve problems in the future.
undermine private wealth and are mirrored $-for-$ in non-government dis-saving.
assist the economy to save when activity levels are high.

are good during recessions because provide direct stimulus to the spending stream and finance private savings.
are good during recessions because they put money into bank reserves in exchange for longer-maturing bonds.
are good during recessions but need to be increased with caution because they increase the public borrowing requirement.
are good during recessions but ultimately require higher taxation in the future to bring the budget back towards balance.