In the table photos, the second one looks much better to me, the first is significantly underexposed. And while the last one is overexposed, the first one looks quite a bit underexposed to me. But it's a dark corner with sunny windows in the background, the contrast is very high to expect even nice exposure straight out of camera.
Here are two tests you could perform. For both, mount the camera on a tripod, or if you don't have one, set it on a table. Just make sure that the scene stays as much the same as possible. The lighting in your first shot is roughly stable since it's artificial, but the framing changed. Sunlight is only reliable if the cloud cover doesn't change during your tests. Also make sure the ISO/shutter are within the range of obtaining a good exposure (nothing red/flashing).
To test for aperture movement issues (aside from looking at it as you take photos):
1) switch to Av, take a photo at f2.4 (the widest); this won't require the aperture to move at all, and should be exposed correctly
2) stop down to f8, and check that the two histograms look similar
If the aperture lever is moving fine, I'd try:
1) Mount the kit lens (18-55), set the camera to P
2) Take a photo, write down the exposure parameters (shutter, aperture, iso)
3) Mount the DA 35, switch to M mode, and set the same exposure parameters; the photo with the prime may look slightly brighter because it's a lens with fewer elements, so it loses less light with internal reflections assuming the coatings are similar. But the difference should be barely noticeable, nothing dramatic.
About metering:
Matrix metering is usually better balanced overall unless you need something very specific with spot metering. Center metering may be more familiar to users of old cameras, and it's the only choice with manual lenses, but it's less accurate than matrix in difficult light (your second example). Manual exposure for the sake of it is certainly not a "pro" thing, whatever that means. M has its purposes but also drawbacks, if you're going to use it, guessing exposure is not that easy, and it's better to pay close attention to what the meter says.
---------- Post added 10-14-18 at 01:36 PM ----------
Originally posted by dieselpunk On the DA 35 it just stays where I leave it. Is this a problem or the difference between zoom and prime?
Yes, that is a problem, they should be operating the same. The whole aperture mechanism relies on the fact that the lever has a spring to close it as far as the camera will let it go. I only noticed this point you made after typing my long response above