Luck will help items with higher rarity drop more often. That means more rare items, epic items and even Legend items. When legend items drop a lot, there is a chance for any of them to be eternal or crystal legend. If you use Eternalized and Treasured Ascension, you will get a lot of eternals given enough time.
Also luck helps items drop with higher item quality drop more often.
650% luck is the cap for luck without Epiphany. With Fortunate Ascension: this 650% luck is still the cap but it's 650+200= 850% luck maximum.
The 1012% luck is because of Fortunate Ascension and Epiphany on both characters.
Epiphany on both characters turns the luck 650% cap into 812.5% cap. The maximum luck with Epiphany (5) on both characters along with Fortunate is 1012.5% luck on adventure page. If you're a solo player, similar principle but the epiphany is on one character.
As for luck at 1045% to 1100% luck, that's achieved by Epiphany (6) to (8) which takes a lot of set slots to achieve with lot more affixes to use for luck and of course Fortunate Ascension. Reason why it's not often used is due to taking up slots meant for Eternalized and other set slots as well as hirling set slots for damage.