Probably.
Here goes my opinions to your questions....
1. I'm not sure what would cause this other then something in one of those other diets causing a reaction or just a disagreement with the food in general...you could try a very bland diet; i..e Innova's sister food California Natural, this is very bland with a lot less ingredients then the others you've mentioned.
2. Hard to say, I have a chihuahua & a pom, 2 out of 4 dogs that have anal gland issues; these dogs have eatin a variety of food....Innova, Cal Natural, Merrick, Healthwise, Avoderm, and now TOTW salmon formula, as well as many different homecooked recipes including all kinds of vegetables/meats/and a tiny amount of grains on occasion...they still have to have their buttocks expressed every few weeks. Just rule of thumb for them, I think it's because they are small honestly.
3. Losing of the extra weight can come from slightly decreasing her food intake, or adjusting her food intake based off the treats she's receiving...do NOT put her on a special food for weight loss or less active just cause she's a little stocky..just feed less.
4. The snoring/sounding congested...I've got one dog that does this big time if exposed to Sage, in fact it's actually really scary, because a lot of dry foods are putting sage in the formula...for what reason I don't know. As another victim, my sisters chihuahua had a bad reaction to Cal Natural, don't know why as he's eating Canidae Lamb/rice formulation which contained the same meat source as the Cal Natural....but he started hacking, like he had something caught in his throat..did this for days, then suddenly it dawned on me that it could be the food....bingo!
But, aside from that, my 3 little dogs all do great on Cal Natural...I feed them the puppy version of the lamb/rice, as I have a very hard time keeping weight on my chihuahua.
Thing is, anyone of these things could be linked to any one of the several ingredients in Innova....could be the barley (VERY hyper-allergenic to a lot of dogs), Chicken/Turkey, cottage cheese, etc.
Try a very bland diet...such as Cal Natural, and feed the lamb version to see if she improves..if so, again, could have been any ingredient, but if the improvement is quite drastic, sudden over a few days, then I'd be suspect of the main ingredient causing issue....i.e. chicken/turkey.
Again, do NOT feed a formula for less active or senior dogs; feed her the normal adult version, just slightly less then what you have been.