Breaking down doors (Strength, Active):
This idea i love!
Shove (Strength, Passive):
This is ... interesting, not so fantastic as with doors, but still good one that should be implemented.
Using a Spell Scroll (Intelligence, Passive):
Here i would prefer to restrict them for those class that should be able to use them ...
But some risk of backfire for others seem like interesting idea that should be concidered imo.
Dip (Intelligence, Active):
This i concider as slightly bad idea ...
Not entirely bad, but since Dip is mostly useable for classes that are dumping Intelligence, it seem like it would backfire for everyone who can benefit for them. :-/
Also i personaly dont like the usual way people see Intelligence stat as equality of IQ ... wich is at least odd ... so logicaly i have problem to see my Knight that dump stat wich have no use for him to be stupid enough to "accidentaly" burn his whole hand, instead of Dip tip of his sword to fire. :-/
So ... concider Itelligence OR Dexterity OR Constitution whatever is higher ... so you are either smart enough to use it corectly, OR agile enough to avoid backfire, OR durable enough to simply ignore the pain ... maybe.

As you sugest it? Nope, sory. :-/
Also i would like to note that soooo many people here is beging for Dip (since Larian will surely not remove that) require some resources ... like we all have countless Grease bottles in our backpack.
Backstab (Stealth, Passive):
This idea i dont like at all.
I agree that Backstab should be re-worked, but this dont seem like good way.

//edit:
Fun fact: I just noticed that you sorted them from best idea to worst one.
