It is without a doubt that exercise does contribute to helping reduce cholesterol (LDL), but please don't have a misconception that if you exercise properly, it will get rid of your problems. While exercising have a lot of health benefits, such as preventing diseases and cancer, to the less noticeable but equally important things in life such as being able to lift your grandchild up into the air without breaking something, exercise will only get you so far. Many people wonder why they aren't reaching their goals such as losing weight when they have been working out like mad. You need to make lifestyle changes to how you do things and change your diet as well, that is more important.
But going on to your questions.
1. This is still something that researchers are trying to find out, they have plausible ideas and clues, but for the moment, the only thing they can say 100% is that exercise indeed does lower your cholesterol levels. Some of these ideas make sense if you know a bit of physiology and the like, but one theory is that exercising stimulates enzyme production that remove LDL (cholesterol) from the body and excrete it. The other is that exercising increases the size of lipoproteins (combination of proteins and fats which can carry cholesterol with it), the logic behind this is that the smaller lipoproteins can wedge between the linings of the heart and other organs and remain there as opposed to the larger ones that cannot "set up shop" between these small areas.
2. Exercising in general, being active more in general will help reduce cholesterol more. I would say this depends on you sir... or miss. Which are you capable of? Some can run for hours, some can run for seconds, some are out of breath walking 3 blocks. If you can run (whether it is on ellipticals, treadmill, or the great outdoors), that is preferred. Studies thus far recommend EVERYBODY in general to exercise about 30 minutes every day or most every day of the week. If you do not have the time to run 30 straight minutes, studies have shown that splitting them off, doing 15 minutes at one point, and doing another 15 minutes later on in the day, still have the same cholesterol lowering effect. It is also stated that the more intense your exercise is, the better effect it will have on lowering your cholesterol, though I assume this is a given. So, if somehow you can run at top speed for 30 straight minutes, go straight on ahead. If not, find a speed that you can maintain throughout this entire exercise, increasing in speed as you find yourself more capable as the weeks go by. You should aim towards cardiovascular, or aerobic exercising such as running and swimming as opposed to weight training or other anaerobic exercises.
Some extra information in case you didn't know that might be helpful or just fun facts.
There are both good and bad cholesterol, which many people may not know about, because of the stigma over the years of cholesterol causing heart disease, etc.
LDL or low density lipoprotein, is one such form of cholesterol. This is the bad type that people really mean when they want to get rid of cholesterol. HDL, or high density lipoprotein (smaller and denser) is the good cholesterol. An increase in HDL apparently helps reduce LDL levels because it takes it away from the arteries, and HDL seems to help protect the heart from heart disease, as opposed to LDL, which we know increases risks. Remember that cholesterol is essential, it rebuilds cell membranes (most of your cell membrane consists of lipoproteins), you just need to ensure to take care of the amount of LDL levels.
Exercising seems to lower LDL, which was already stated, while RAISING HDL levels within your blood, which is a good thing. Another theory of why exercise lowers LDL is because of the increased circulation of blood within your body, increasing the chances of removing these particles from clotting up your blood vessels.
I read that evercising most days out of the week will help lower your cholestorol and your overall risk for cardiovascular disease. About the running versus walking question. The American Heart Association claims that brisk walking or other moderate levels of activity is enough to gain the benefits of exercise. My dad has high cholesterol and his doctor told him to also watch out for his diet. It is definitely a good idea to get your body moving but don't forget to watch what you are eating because that can greatly impact your cholestrol levels. I have found tons of great websites about cholesterol and excerise if you're interested.