First, shields, I do not agree these should scale, I do not see a reason for it, I don’t feel like I take more damage in M10 than I did in M4 on Mayhem 1.0. Infact, under specific circumstances,
mobs on Mayhem 1.0 M4 did more damage, the obvious example being the double projectile modifier, if you were careless in M4 it was very possible to just get instagibbed by a Badass Zealot rocket with double projectiles.
I have yet to get instagibbed by any mob or boss on M10 lol.
And yes, emphasis on mob, I’ve killed myself with Anarchy’s reload, and my Boom Sickle multiple times lmao.
I do, of course, have a feeling there’s one particular mob that will likely be the first to instagib my poor booty, Anointed Goliaths lol.
Nades yes, they should get the same treatment as weapons, maybe slightly less of a boost because of the new anoint, but that is all entirely dependant on if that anoint does cause mayhem boosted grenades to be far too powerful, I don’t know if they would be. 
Classmods I assume you mean? I don’t know about buffing these, at least not the stats on them.
The stats are already helping you, and after farming for my “BiS” mod, I’d hate to go through all that again just because the stats increased a little bit lul.
I would not be opposed to something cooler though.
Like “anoints” on classmods that are entirely unique to them. One anoint could be an adaptive anoint that does something unique to whatever action skill you’re currently using, basically its one anoint but the effect (and description) changes depending on what action skill you’re currently using (so its not too annoying to farm, adding yet another layer of RNG to classmods).
Another one could be a simple +1 extra point to one of the skills the mod is currently boosting maybe? Though this would likely have limits, as I believe seeing some mods can increase single point skills, like Amara’s “Find Your Center”, which would MAYBE boost melee dmg too much (if they fix mayhem scaling on melee), but that’s just a maybe, if it doesn’t do too much then awesome lol.
Yet another one could be a buff/added effect (latter more interesting of course lol) to the capstone in the tree you have most points in. 
Basically, all of these would be adaptive, there wouldn’t be an anoint for every capstone or action skill, the “anoint” would simply just boost whatever you’re using (and change the text to let the player know what the anoint is doing, especially if they add new effects, AKA the cooler option.)
There’s a ton of cool things they could do with something like that, and even if farming for god-roll stats again would be annoying, I’d be fine with doing so if something like this was added, because my current class mod will still be good, I’m just missing out on a bit of a buff to the class. 
As for labeling items with its Mayhem Level, yeah, that’s a bit of an odd one, kind of just feel like they forgot. 
But, a shameful plug incoming, I’d love this even more so than labeling what mayhem level an item is:
So if someone could bump it, I appreciate you.
Though yes, labeling them should still happen, I just wanted to plug the thread lmao.
Haha, thanks!
I did forget I made that post, and so I read it again, and I would still love something like this lol.
Think I’ma copy-paste it into its own thread lol.