The premise of your question is incorrect.
In XCOM: EU, savescumming was possible so long as you didn't move, as the seed was generated upon squad movement, and thus it was possible to reload saves over and over to get the desired outcome.
This is false. The seed is generated at the start of the battle - it has nothing to do with whether or not you've moved. Doing the same actions in the same order would always cause the same outcomes, so the method of save-scumming you mention would not have worked.
However, it is still possible to save-scum in XCOM:EU by taking different actions. For example, if unit A misses their shot, reload, have unit B do something, then try the shot again with unit A. This method of save-scumming still works in XCOM 2.
For more info, see the Random vs Seed article on the XCOM:EU wiki.
It's also worth mentioning that XCOM:EW added a "second wave" option called Save Scum, which generated the seed on every reload. Using this option, if a unit misses a shot you can simply reload and try again.
In XCOM 2, there are two mods that do the same thing. One works automatically, but is written in a way that makes it incompatible with a lot of other mods; the other restores compatibility at the cost of having to click a button.
No, doors provide no cover. Once opened they remain opened even if closed.
I found this when playing a UFO mission and two soldiers either side of the UFO doorway. I opened the door to 'spawn' the enemies inside, which they did. Then I closed the door, hoping to limit their ability to hit me and force movement.
The next turn a Viper pulled one of my troops directly through the closed door with it's tongue attack, and ADVENT troops shot through the door at my other squad mates.
Best Answer
Not After Every One
Successfully hacking something will not automatically increase your specialists' hacking scores.
Just When It's the Reward
When you are hacking an objective, the listed reward will sometimes be "Enemy Protocol". This is a permanent boost of 20 to the soldier's hack stat. You need to select this as your reward and succeed in order to get the boost.
From my own experience, I can say that the boost is applied immediately. Any further hacks the same mission will be easier.
This is mentioned as one of the ways to increase a soldier's hacking stat in Chris Hayes' answer to How can I raise a soldiers hacking ability?
Reports Otherwise Were Untrue
I've found some reports of getting a small increase in hacking skill after every successful hack, but, as discussed in this Reddit thread, that was likely confusion from the increase in hacking your specialists get every time they are promoted.
In that thread, multiple people report testing this idea, and finding that successfully hacking did not automatically increase hacking skill. One even inspected the source code. Chris Hayes has also checked the source for this bonus, and says that "I've searched repeatedly and can't find anything at all to support it."