Has anyone had a problem with the Pac not dissolving and clogging up the hose with residue?

Yes! I think I've just learned a hint that might help you. Of course, have your water temp hot enough (120-140 degrees F) and clean your filters and spinner arms regularly. Helpful Hint: once dishwasher is completely loaded with dirty dishes, take a paper towel and thoroughly (obsessively??) wipe dry the dispenser where you will put the Pac. If there is any moisture at all, the Pac may begin softening/dissolving, but then hardens when the heat,even of the water, begins. Then the Pac adheres to the dispenser or only partially empties, hardening rather than dissolving. (I obviously don't know the science behind this, but after 2 months of having to do all our dishes twice, I am so relieved to find a simple answer to an annoying and wasteful and inefficient situation. Good luck!

Do you have to use salt with this product?

No pepper is required either! It comes pre-seasoned!

Do these pods just get thrown in the dishwasher?

Dishwashers have a pre-rinse cycle before going into the wash cycle. That its the reason for the detergent compartment. If you don't put the detergent in the compartment then it will be washed away with all the pre-rinse water and food waste and will not be available for the cleaning cycle. So, no... Don't just throw them in. Put them in the compartment.

How do you decide which strength of pod to get? Eg 15x vs 12x vs 10x. Why would you not just get the most powerful one?

It depends on what you're washing. Lots of dried or baked on food? Yes, stronger. A lot of glassware and just-used dinner plates, NO! The stronger tablets have more grit and will eventually cause your glassware to get cloudy from abrasion and the paint on your coffee mugs will get worn off.