Cactus ID please?

[NorthernCacti]

This cactus was started by my Grandmother some 40 years ago and given to my mother as a 6" plant. I got it as a 8' tall plant 3 years ago. Under my care it survived house reno's and moving in freezing temperatures 10 hrs away. I have done nothing to it but water it(0.25gal/weekly). I'm in construction, and by no means a gardener. I just take pride in having a plant that my Grandmother started.
1. What kind of cactus is this?
2. Are all the brown spots normal?
3. Does it want full or partial sun?
4. The stray branch started leaning a month ago, what gives?
5. How much/little water does it want?

thanks for your input
~NorthernCacti ~

[teo]

1. Euphorbia trigona (so not a cactus)
2. I think they are just signs of old age. The brown at the bottom is corking