To be honest, looks pretty generic. I especially dislike the lack of available skills… 5 is it?
Actually, it's more like 1 skill per class and use consumable for the other ones if you wish to use them. I hate how these work (and I think a lots of people do too). The good news is that the Foundry missions can do skill checks.
I didn't view the entire video - are there puzzles as in DDO?
I encountered 3 small puzzles while doing the main quest at low levels. People can probably do lots more with the Foundry though. And the Foundry is going to be the main part of this game. I did one small campaign by an alpha player and it felt like a small module for NWN.
With so few hotkeys, how are the many spells of a D&D wizard handled?
In 4e, all classes have powers (spells/prayers are powers) with different usage frequency: daily (once per 8 hours or 3-5 encounters per the books), encounters (once per encounters) and at-will (at any time).
In NW(O), the daily have an action point meter that fill up at about the rate of full after 3-5 encounters. The per encounter have cooldowns of a about 12 seconds (I saw a few higher). At-will are the left/right mouse buttons and have no cooldown. So a Wizard could have 6 spells, but selection from the encounter pool (3), at-will (2) and daily (2, but can only use one at a time because it drain the action-points). Each class also have a 2 special "ability" as well. One drain stamina and is to avoid damage (dodging basically, although the Guardian Fighter have shield use). The other is more of a "power boost" for a time that you gain at level 10. Cleric have Channel Divinity, it change the behavior of your abilities. Rogue have stealth, which increase attacks damage. I didn't bring my Guardian Fighter to 10 to find what was his "tab" ability.
Are they sticking to a low magic setting or are they going crazy and bloated with 40 strength scores as DDO has done?
The game is in Neverwinter, Forgotten Realms 4e D&D (so not low magic), but it's different from DDO as well. 4e is quite different from 3.5e, more streamlined. Currently, using level up stat point and a base score of 20 (18+ 2 for racial) you can get a single stat to 27. This is on the 5 level stat points you get and there are two case of +1 to every stats as well (from what I've gathered these are in 4e D&D). No idea about items stat bonus, but up to level 20 I haven't seen anything special.