I am using the Mitsubishi projector calculator and hanging the HC1500 from 7 feet height and 14 feet away and the screen is like 1 inch off the ground. This is for a 120 inch screen (diagonal) The thing is, that the top of the screen is only at 5 feet (so 2.5 feet to spare).

Is this literally what will happen, or can I easily tilt or adjust the projector to move the screen up the wall, so the bottom of the screen isn't on the floor?

Will tilting the projector ruin the aspect of the rectangle?

I am brand new to projectors and trying to plan out the construction of my basement. Can I physically just tilt the projector a bit to centre the image on the wall, or will I need to reduce the screen size?

You just need to angle the projector up, and use keystone to correct the image shape.

It is better to tilt the projector up and the screen forward and avoid digital keystone correction as it degrades PQ. This may degrade the gain on your screen as well, depending on what kind of screen you have.

It is better to tilt the projector up and the screen forward and avoid digital keystone correction as it degrades PQ...

I had to tilt mine up slightly due to a low ceiling (7' 6"). I ceiling mounted mine with the shortest height mount I could find and project onto a 107" screen from 14', and I use +3 vertical keystone correction.

I can see no negative effects of using keystone correction when viewing video/film material.

Viewing computer graphics material from a PC source may be different story though.

I'm sure that keystone correction in general is not a good thing to use as it "Post Processes" the image, adding potentially undesirable video information that was not there originally but in my case, with what I view, I can see no difference when I use it in moderation and this allows me to have my screen mounted higher than would be otherwise possible.

You didn’t say for sure you have the HC1500 yet it sounds like you are in the planning stage. Not all projectors have the same drop height some are better suited for lower ceilings.

If you do have that projector I would slightly tilt the screen as mentioned above if it is a fixed screen. based on what you end up with for seating and screen height a slight tilt might even line the screen up square to your eyes better. Also look for a mount as mentioned above that hugs the ceiling but make sure you still leave the recommended air flow distances around the projector.

Tilt the pj as slightly as possible, IIRC you should not tilt it more that 10deg..Because it can load the color wheel and cause bearing wear....If you have a drop ceiling in the room you can remove a panel and mount the pj recessed into the ceiling as much as possible..