I've got a 5.7 in my AWD 300. I've always used Mobil 1 Synt, EP Synt or HM Synt (what ever Mobil synthetic is on sale, I usually buy a bunch for a few changes,) and Mopar filters.
I've wondered about using 5W30 and if it would affect much, but not tried it yet as I'm still in warranty (for another week

lol)...
Well, you're not using MS-6935 approved motor oil anyway, so just based on that, the dealership could deny your warranty claim. The Mopar filter for the 5.7 is a cheaper Purolator design. If you want better flow and good oil pressure, upgrade to a Purolator BOSS PBL24651, or Royal Purple 20-820, or Fram Ultra XG2 (Titanium FS2), all synthetic media filters. They are bigger and allow for more oil to flow, which is key for these HEMIs. The only reason why the filter was shrunk was due to the electronic steering, but it was a dumb move since, with some effort, you can still install the bigger filters. Going up to 5W-30 won't hurt anything, and if you drive in a hot climate, it helps a lot. Of course, if your HEMI has an oil cooler (on the 5.7, it's usually above the oil filter), then you should be fine with 5W-20. Getting the dealer's warranty service has a lot to do with the relationship you have with that dealer, which weighs a lot in their willingness to help you, more than what oil you use. As long as you don't dump Lucas by the bucket load along with 20W-50 and an "orange can" for an oil filter, you should be fine.
In theory, yes. In practice, the average consumer does not have the time or financial resources to fight the OEM once coverage has been denied.
As I said above, it depends a lot on your relationship with the dealership. Warranty can be denied for any reason, and if they want to, they will find one without much effort. The same goes for if they want to help you, they will properly document your claim, including taking pictures of your engine internals, which clearly shows abuse or improper oil changes.
Speaking of preaching and pontificating...
Pontificating and preaching is when someone pushes others to use a certain oil or oil viscosity or do things a certain way. Like telling people to use "what the manufacturer recommends" or "MDS will not work correctly if you don't use 5W-20 MS-6935 approved motor oil." Both of these statements are bollocks. It's called a recommendation for a reason. It's not an automatic transmission. An internal combustion engine is subjected to different loads. People run whatever gasoline they can afford or get in these engines, so motor oil is also subject to change based on ambient temperatures and engine loads. I'm just trying to tell others that they have options and use their best judgment when deciding what lubricants to use. Everyone has a different use case and application. As to MDS, for the solenoids to operate properly, they need clean oil, and for the lifters to disengage, they need good oil pressure. Any oil like 0W-20, 5W-20, 5W-30, 10W-30, 0W-40, and 5W-40 can provide these, heck, even 15W-40 under the right circumstances. Going thicker could damage the screens on the solenoids.
Last month I met a guy who was driving a pristine looking 2015 Dodge Charger R/T. It was stock, his daily driver. The engine sounded real good. I asked him what oil he was running in it, and he said Castrol EDGE 5W-40 with the bigger Mopar filter. I asked him how many miles, and he said 140K and some change, and he does 5~6000 miles OCIs. He said he wants to get at least another 5 years out of it, and he drives a lot.
Everyone who can't afford a new car every two to three years will do their absolute best to protect their investment and get the most out of it. Far be it from me to tell others what to do. That doesn't mean that I can't share my opinion and do my best to help others.