Legion's pre-patch is going onto the PTR, which is a pretty good sign of progress. The expansion is coming out at the end of August, meaning that this patch should probably be coming out in July.
As far as I know, while those who have pre-purchased Legion will be able to create their Demon Hunter characters during this patch, the PTR tests don't appear to allow you to take them out for a spin.
You will, however, be able to try out all the existing classes' new talents and spec designs. I'm definitely most interested in trying Prot Paladins and Frost Death Knights (for obvious reasons,) but I also want to get my hands on Outlaw Rogues, Survival Hunters, and other specs undergoing serious redesigns.
The new transmog system will also be available for testing, and I would assume the pre-expansion event.
I'll probably update this post when I get my impressions.
So I've now done a bit of light testing, and while I've tried out several classes, I've focused primarily on DK Frost and Prot/Ret Paladins.
Frost feels similar, especially if you played Two-Handed, given that Obliterate is the big strike. Killing Machine will now only affect Obliterate, so it's hard to waste it. You'll probably still want to keep two runes available for it. Remorseless Winter is basically the new Death and Decay for the spec, which is centered on you and moves with you. For the most part, however, the spec feels the same.
Protection Paladins I'll obviously have to wait to actually tank something on, but rotationally even though so much has changed, it doesn't feel completely alien. You no longer have Holy Power, so instead you just pepper in your Shield of the Righteous when you have stacks. Having my addons back will help a lot, as they let me track if SotR is up and for how long.
Hammer of the Righteous is quasi-merged with Crusader Strike, and you'll technically have to be standing in Consecration to get it to AoE. However, two of the three talents related to the ability negate this problem - one replaces it with Blessed Hammer (see Diablo III,) and the other removes the cooldown and makes it always AoE, so it's really more of a choice to have that issue than a choice not to.
Holy Wrath is gone, but I think that the HotR talents will give you some snap threat options, but obviously it all depends on how our threat compares to the DPS.
Retribution feels pretty different, though not in a terrible way. Exorcism has been replaced with Blade of Justice, a long-ish cooldown strike that hits hard and gives two Holy Power. Judgment I don't think gives HoPo anymore (but BoJ's two HoPo generation makes up for this) and looks a lot different but plays a similar role in the rotation. Judgment can be talented to do a little splash damage, but I think the main source of AoE you're going to get is Divine Storm - but you'll be able to do it often enough that I expect it will still let you pump out a decent amount of damage.
I tried to do the Broken Shore scenario, but it seems to be bugged - you can do the quest that leads up to it, but you never get put in the instance.
Oh, and the Stormwind Park has been rebuilt, and it looks very different than the old one (read: better.)