How does cutting your lawn without bagging the clippings benefit the lawn?
Can these clippings promote new lawn growth?
What height setting yields the healthiest grass?

Stupid question but how do I know what type of grass I have?
I suppose Fescue is just a fancy word for grass? haha

If you live in the northern 2/3 of the country chances are high that you have a cool season grass like Fescue or Kentucky Blue Grass (you see it abbreviated as KBG a lot on forums). Cool season grasses for the most part stay green all year and don't grow well much below the upper 1/3 of Georgia, where summers get too hot and kill them off. I live in metro-Atlanta and growing Fescue is a constant struggle because of the heat and usual watering restrictions due to drought in summer, but its the price you have to pay if you don't like an ugly brown lawn for 5 months of the year and don't want to overseed Bermuda, etc. with Rye Grass during the winter. Warm season grasses like Bermuda, Zoysia, etc. go dormant and turn brown about the time of the first frost and generally don't grow well in cooler climates.

Northern Grasses (cool season grasses)
Fescue use in lawns is a fine bladed bunch grass. It will tolerate more shade than other northern grasses and will remain green through most winters. It will not spread appreciably and usually does best when overseeded every fall. Mowing height is as high as you can get. Start there and adjust but don't go to the lowest setting.

Kentucky bluegrass is a fine bladed sod-forming grass. It will spread to fill in any bare spot. It goes dormant in the winter and turns brown. Mowing height is 3 inches. Adjust from there.

Ryegrass is used mostly in the Pacific Northwest. We don't see much concern about it here in the forums. It is either the perfect grass or it isn't used much.

Southern lawns (warm season)
Bermuda is probably the most popular grass around if, for no other reason, it is extremely hardy and very tenacious. If you had a different type of lawn and it got some bermuda in it, you likely will have a bermuda lawn in a year or two unless you know how to stop it. It is a fine bladed, sod-forming grass that works best mowed twice a week minimum. Mow it at 1 inch or less depending on the cultivar. In order to look best bermuda needs monthly fertilizer with a high N number. Bermuda will turn brown in the winter and will survive any drought.

St Augustine is my turf and my favorite southern grass. It is a coarse bladed, sod-forming grass. Mow at the mower's highest setting and water it weekly in the summer. If it is watered weekly all year, it can remain green and growing in the warmer parts of the south. Otherwise it goes dormant and turns brown. It cannot survive complete drought. Let it dry out and you are in trouble.

There are other types of grass, but these are by far the most popular.

Always mulch mow your grass. It has been said you can save 1/3 of your fertilizer by mulch mowing. Not sure I go along with that but what would be the reason to remove mowed grass?

When you ask questions about your specific lawn, it really helps to know what town you live in I (or near) and what kind of grass you have.

Does it hurt to mulch a yard that has severe brown patch?

Thanks in advance.

As for mulching using clippings...that's alright if the grass has not been given a fertilizer that might disrupt the growth pattern of the plant given it, or the grass has not been given a herbicide to kill unwanted weeds--which would surely not do the plant that is next to it any good, or the clippings leave the area looking like a barnyard, or when it rains, the clippings don't take on a matted look of waste and next to a plant trying to make it into the world dies from being smothered, or....??

Grass clippings are much better given to the compost pile where it is one of the best ways to heat it up.
It contains all that nitrogen...in itself, and in the fertilizer we give it.

Some types, notably kentucky bluegrass, given nitrogen, can cause thatch buildup and the more clippings that don't break down within a short time then adds to the thatch amount. But, given that result, it still best to feed the lawn and leave the clippings on the lawn.
The height of growth is different for different types of grass. Two and a half to three inches is fine for K.B....but you wouldn't do this for 'bent' grass...the type seen on golf greens.
All the types of cool season and warm season have their set of what height they should be given....and the times they are cut at.

One thing I do agree with, after a lot of disbelief...is to take the time in the spring to have your mower blade sharpened. It makes a difference one can see.....and appreciate.