I cut my gaming teeth on 2nd Edition ...
I've been asking myself whether 5E might be right for me and my campaign.
You started with 2e? You didn't hate it? You were able to play 3.5 successfully? Yes, 5e should be just fine for you.
My chief concern is of how well the system will work with my campaign world. The campaign is intended to be low magic, a setting in which arcane casters and magic items are a rarity. Divine casters are somewhat less rare, but still a very uncommon occurrence. How well would 5E support such a world?
It depends on to what extent you want that 'low magic' - more importantly 'few casters' - aspect to be reflected in the party. If you would have not trouble with everyone in the party being a caster - their 'uncommonness,' perhaps, brought them together - then 5e, with it's default assumption of few magic items, tightly controlled by the DM, and most PC options being casters, should be just fine.
However, I have seen a lot of character examples in which classes that I would not normally associate with magic by default have some level of casting abilities.
Yes. All classes have at least one sub-class (typically chosen at 3rd level), that innately uses magic in some way. There are 5 PC options, out of 38, that don't have any magical abilities at all: the Berserker, Champion, Battlemaster, Thief & Assassin.
Would it be possible or even reasonable in 5th to have a party of six players with only one character among them who has access to arcane spells? And one with full access to divine, or maybe two with limited divine ability?
Possible, yes. You could have a party of all Champion fighters - anything is possible. So is a party who all cast arcane spells. Like I said before, there are 38 sub-classes. 17 of them cast arcane spells. If you aren't careful to coach players against choosing those sub-classes - or don't just ban some of them outright - it seems likely you'll get a couple.
Can rogues, fighters, etc. be played completely without any magical ability?
Yes. They have the most non-magical options, at two each.
Would placing such restrictions on a group severely limit character options, or does 5th give enough non-magical choices for characters to still offer some variety? This alone is probably the issue that will determine whether I convert over to using 5E.
No magic at all does bring it down to the 5 sub-classes I mentioned. Magic, but not actual casting, opens up the Totem Barbarian and Open Hand Monk - possibly the Shadow & Elemental Monks, as well, if you don't consider their use of spells (powered by Ki points) identical to casting.
It's not like 3.x or 2e is a lot better. In 2e, you had fighters & thieves not using magic - basically the same boat as 5e. In 3.x, you added the barbarian, and, later, Knight and Scout. Still only adds up to about 5 non-casters, though, obviously, you have a lot of build options.
What you do have in 5e is Backgrounds (very like 2e Kits). A different background can make two Champion fighters more distinct from eachother - if one's a woodsy Outlander and the other's a lofty Noble, for instance.
While not nearly as pressing of an issue, I did have another concern with one 5th Edition mechanic I had been reading about: the Advantage/Disadvantage system. I don't think I've read a single bad thing about this system, and from what I've seen it seems to be universally liked as a useful simplification over previous systems (which is a good thing). I understand the basic mechanics of it (roll 2d20, use higher or lower depending on situation), but I admit I don't have a good knowledge of what all determines advantage or disadvantage.
That's largely up to the DM. 5e is very like classic D&D in that the DM makes a lot of round-to-round rulings on the fly. It's not quite as codified as 2e C&T, let alone 3.x/Pathfinder. In general, you could rule that anything that formerly deprived a creature of DEX bonus to AC would grant attackers advantage (and give disadvantage on REF saves, for that matter). Except flanking, though that's also an optional rule in the DMG.
It's a long shot, but it's their best hope. One player tosses the die, and... natural 20! Almost certain defeat has been turned into a victory! Yes, it is a rare situation, and even rarer that it works out in the players' favor, but at a 1/20 chance it is still enough within the realm of possibility to offer hope
With the Advantage/Disadvantage system, I think that moments like this will be lost. It seems to me that if the players are in a tough situation, they are likely to be disadvantaged, and as such that 1/20 chance gets turned into a 1/400 chance
Adv/Dis is a binary state, so if you can come up with one source of advantage, you negate any amount of disadvantage.
Is the Advantage/Disadvantage system a part of the rules that can be omitted in favor of something else?
Everything is. You could very easily replace it with a simple +2 modifier for Adv, -2 for Dis. You could keep it non-stacking/binary, or you could let those mods stack. It's not even mathematically /that/ different (Adv/Dis is a little complicated to analyze, but it works out to being equivalent to about a +/-5 if you were 50/50 to start, down to a +/-1 if you need a natural 20 to succeed or 1 to fail).
1) Does 5th Edition work well with a low magic/rare caster campaign
Low magic (or low wealth, BTW), yes. Rare casters
enforced against PCs, no. In addition to the emphasis on magic in the PC options, healing requires a reasonable amount of magic - though that should be familiar from the other editions you've played, which is, perhaps, why you didn't ask about it. 5e actually has a few options that let you get by on non-magical healing: If you use the optional feats, there is a feat that lets a healer's kit restore hps instead of just stabilizing and another that gives a bonus to healing during a short rest. You have 'Hit Dice' (the same HD you use to generate you hps) that you can spend after a short (1hr) rest to heal yourself. And, by default, 'natural' healing restores all your hps overnight. So out-of-combat, you can get by without a caster able to toss healing word or CLW around. Effective in-combat healing still comes almost entirely from magic. The one exception I can think of is a single-use, rest-recharge fighter power, Second Wind, that heals 1d10+level damage as a bonus action.
and 2) does "Disadvantage" really rob players of those epic "one crit saves the day" moments?
Seems unlikely it'd do so. If the party was desperate and at disadvantage, they could still have one character do something to give the 'hail Mary' attempt advantage, and thus negate the disadvantage.
On balance, I'd encourage you to give 5e a chance.