Answering your first question: let your parts compatibility and priorities do the downselection for you. It sounds like you are hesitant to avoid modifying the dial, so this means you'll be using a 3135 movement instead of a 28xx movement.
Take a look at these web pages on Ranfft which have details about the movements you're considering, and take a look at the dimensions under "data." Look through the link "comments about the data" underneath to understand what each of these parameters physically refers to on the movement.
http://www.ranfft.de/cgi-bin/bidfun-db.cgi?10&ranfft&&2uswk&ETA_2824_2
http://www.ranfft.de/cgi-bin/bidfun-db.cgi?10&ranfft&&2uswk&ETA_2836_1
http://www.ranfft.de/cgi-bin/bidfun-db.cgi?10&ranfft&&2uswk&Rolex_3035
You will understand that a case designed to fit a 2824 might not fit a 2836, and might not fit a 3135 movement. This is because of different stem heights and diameters of the movements. Clever uses of spacers/shims can allow a case to be used for multiple movements, but unless there is an explicit statement in the listing saying it'll fit a 3135 movement (or unless you have confirmation from someone knowledgeable), I would not buy that case. Focus on finding a case that will fit a 3135 movement.
To answer your second question: it would fit the movement you want to use, but it's possible your dial will be too small for the dial opening in the case. In a watch the dial with diameter D is pressed against a "dial lip" which has a diameter slightly lower than D. This means the outer periphery of the dial is hidden underneath the dial lip when viewing the watch from in front. If your dial is too small, it'll "fall through" the dial lip into the area underneath the crystal, and this means the whole movement/dial assembly will be floppy within the case (i.e. this does not work, you must find a case that fits your dial). If you know the diameter of the dial that's supposed to fit that watch, and if it's within a small range of your dial, then it'll work. If the case is cheap enough you could buy it, get some calipers, take some measurements, do the same with your dial, then draw a conclusion.