The lime raises pH and provides a source of Ca and Mg, which are often/usually missing in soluble fertilizers. There's more detailed info in the thread about container soils. If you haven't read it and wish to, I or someone else will provide the link.

Al

For the most part there isn't any real difference between various sphagnum peat products. There are brands that offer a more coarse cut, but they are hard to find. Because it's a small component, I wouldn't worry about it much.

Not trying to confuse you, but I don't use peat in my mixes at all. My own version of the 511 mix is bark plus turface MVP. It is a little more pricey than the 511 mix, but the water retaining ability of the unscreened turface compensates nicely for the peat and removes the need for perlite. It's simply another option and results in a coarse mix that retains a lot of water internally. It's what I use for annuals and veggies for outdoor summer growing.

I opt for less water retention and more structural stability for perennial plants, particularly those that will spend winter in my basement growing under lights.