Does this work within the rules?

Is my reminder text worded correctly?

Yeah, I think that all works. Nothing wrong with granting evoke to cards in hand. Wizards might try to include the reminder text for in a separate line at the top, but apart from that I think it's fine within the rules.

Whether it's fair is another matter entirely. Some good cards to use with this: Bogardan Hellkite, Reiver Demon, the Myojin, Dread Cacodemon, Hound of Griselbrand, Vorapede, and especially Ashen Rider :) And on the "forgotten cards" side, Petradon gets to do a nifty 3-mana Rain of Salt thanks to stack tricks. Not as good as Woodfall Primus though, which does the same and leaves you a 5/5 trample too.

To most of those, I just have to say "Yeah, but Elvish Piper exists" (Though this is colourless or blue; which is kinda odd.)

Five mana and six life seems like a fair enough cost to drop a critter straight into play. This maybe ought to tap though, to prevent the worst tricks.

­Reiver Demon and Dread Cacodemon have the "If you cast it from your hand" rider, which this bypasses nicely because evoke is a way of casting such things. Some others like Ashen Rider and Woodfall Primus are just me being a Johnny and taking advantage of the way the creature is sacrificed, which would obviously be a drawback in most cases...

Five mana is Wizards' cost for dropping a green creature onto the battlefield: Dramatic Entrance. But it makes a difference having that mana be spread 2 on turn 2 and 3 on turn 3.

This is probably within Wizards' power bracket for a mythic. (Modulo Phyrexian mana evergreenness and issues of whether this is in the right colour.)

Heh. It's true. This, Emrakul, the Aeons Torn is probably game. Add a way to return it to your hand every turn, and, if your opponents are tapped out, then its an automatic victory at your multiplayer table. That getting around the "When you cast" clause is unfortunate. I think the artifact is a really neat idea. Maybe it should replicate what evoke does without actually calling out the keyword? Just ": Put a creature from your hand into play, then sacrifice that creature."? That way, you not only solve the Emrakul problem, but the card stops being broken with Vedalken Mastermind.

I decided to go in a less complicated direction with this card. Because you're technically "casting" when you evoke a creature, does reducing the cost to evoke a creature work within the rules like this?

Yep, this should work fine.