What are the properties of "gear"?

As an example, my MH weapon is:
“Golden Axe” in red – obviously the name
“9696 DPS” in yellow – damage per second
“Cleave” in purple – main skill of weapon
“MP: 910” in light blue – amount of mana points required to use the weapon?
“(3) Golden Veins” in green – It appears these are “set affix” properties and 3 is the “rank”.
5 items in orange – Affixes From what I can tell, Red are Legend, orange are Epic, and yellow are Rare. Is there a list of all of these affixes and how to get a particular affix?
“ILVL 100 and 25.6k” (in white) – obviously level and amount I can sell the item for.

Questions: How do I increase “rank”? How can I get a list of each of the classes of affixes and their min/max value (I found a list on here, but the values aren’t correct or are for one class and I’m using another)?

There are no class specific affixes. To get another rank of a set affix, put that affix on another piece, or the legendary affix +X to all sets, or the final MS added to a piece of jewelry gives the same effect.