1) Allegro supports rotated sprites, but only with its own sprite objects (i.e. you have to either provide or create a seperate "sprite" image for these functions rather than grabbing the image data from a composite sprite sheet
2) Allegro's window management utility is a little bit primitive, but if you're smart then you can override its built-in "winmain for dummies" with one of your own for extra control. I don't bother to do this though. At a basic level, it's extremely easy to set up a windowed or fullscreen application to run at whatever colour depth you want and at (almost) any resolution.
3) Parallax scrolling is easy enough to achieve algorithmically (that's how Pixel did the moving clouds in BkMoon) so your implementation should have little effect on that.
4) In my experience Allegro's digital sampling (sound effects) always seem to come out really quiet, so you may want to test that out to see if you're okay with how it sounds before making a commitment. As well, it has very little built-in support for audio playback; it does MIDI, and an audiostream thing that looks pretty low-level, neither of which I've bothered to deal with since I simply use the PxTone library. However, there are extensions to allegro I can see that give MP3 and OGG support.
5) Allegro doesn't really give any high-level support to the game development process; it has no special functionality to deal with interpreting maps or entities or collisions or any of that stuff; it's just focused on giving you the basics (drawing to the screen, interpreting user input, basic GUI, sound support) that you can use to build your own engine off of.
I've never checked out Construct so I don't know what kind of background you're coming from, but in my experience Allegro is a great graphics library with some interesting perks (packfiles, portability of the (basic) library, some nice addons) but needing supplementation in sound/music support. Basically it covers up the most low-level actions needed in developing a game.
If you want to learn more about what Allegro does, I'd recommend you check out the manual:
http://alleg.sourceforge.net/latestdocs/en/allegro.html