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-kytz-r, u, b, l, d, f are 'wide turns'. Instead of turning a single layer like in R (L, F, B, D or U), you turn two layers. Sometimes, 'wide turns' are also written with capital letters followed by a 'w' (e.g Rw, Lw etc). You'll get to see a lot of algorithms with these type of turns once you learn higher degree cubes (4x4 and onwards). Wide turns are also known as 'double layer' turns.
The brackets are usually used to denote triggers. Triggers are combinations of algorithms that can be executed with finger tricks. People tend to optimize algorithms based on triggers so that it can be executed very quickly and it aids memorization. The second algorithm you listed is for solving an OLL using (L' U' L U) triggers which is normally for left-handed cubers. For right handed cubers, they tend to prefer a y F (R U R' U') (R U R' U') (R U R' U') F' to solve the same OLL.

y, x and z are cube rotations. This is where your turn the whole cube according to the respective Cartesian axis. Imagine the 3D axis of x, y and z going through your cube (y-axis goes from top to bottom, x-axis going from right to left and z-axis is the axis that's coming towards you). a y would mean to turn the cube clockwise along the y axis. Yeah, it's a bit hard to explain in words and I'm too lazy to google for a good image.

Anyways, the current record holder for the Asian 4x4 and 5x5 blindfold once gave me this quote:-
QUOTE(masterchesterlian)
overthoroughness becomes confusion.
x = triple layer R
y = triple layer U
z = triple layer F
That helped me a lot to figure out which way a cube rotation goes.
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eXPeri3nc3Dont go for color neutrality. In my opinion, that is only for the most gifted cubers (like the Australian kid who holds the current sub-10 world average. holy crap, he's fast). I know a lot of people that get disheartened and gave up cubing when they tried to be color neutral.