IME when using roll-under it's either a d% roll (e.g. Thief skills) where either
a) the player doesn't know any bonuses or penalties that might be applied due to current in-fiction conditions etc. (e.g. the DM might decide the rain-slick stones make climbing 10% harder, the rain-slickness will have been narrated but the specific penalty won't be) or
b) the DM has noted the target might be different than usual e.g. instead of "Roll under your Dex to cross this slippery bridge" it might be "Roll way under your Dex" or "Roll under half your Dex".
This depends on the table. Plenty of GMs will tell you if you have a penalty to the roll. Plus, well, in a roll-under game, if you know you have to roll under a 15, and you roll a 13 and that's a fail, then you also know you had at least a -2 penalty. If that happens enough times, you learn "rain-slick" equals -2. Or -10%; either way.
It depends on what the system's being used for, I think, and just how much of it you want to have be affected by the character's level.
For me, some things like the ability to notice something are almost intrinsic to the character and don't change with level: a 10th-level Fighter has about the same chance to notice something as a 1st-level Fighter. (exception: Thief-types who specifically get trained in such things, as reflected by their increasing skills as their levels advance)
Meh, this is a "your mileage may vary" kind of thing. One could easily say that adventurers become more aware of what to look out for--what that faint rustle in the trees or slight movement of shadow or that look between those people
mean--as they level up, so it makes total sense for a perception score to increase.
That, and at least the games I'm used to don't use straight 3d6 for stat generation but instead use somethng more generous as per either the 1e or 2e DMG (or similar).
Right, but that's your table. You have to realize that your games are apparently quite different than others. I've looked at plenty of OSR games that not only demand 3d6 in order, but if you rolled a sufficiently high number, like a 15 or higher, then your
next stat must be rolled on 2d6. So if that's your exposure to roll-under systems, and your character's stats are
designed to be very low, then it becomes unfun to fail all the time.
I personally think that's a dumb way to design the game, because you can very easily just give penalties to certain tasks which do the same thing, while at the same time allowing characters to succeed at less-difficult tasks and therefore feel like they are actually accomplishing something.
And if someone does have a 6 in a stat then failing rolls related to that stat should be de rigeur.
But even if that's an accident of bad luck--like you have a 4d6-drop-lowest-and-assign-as-desired and managed to roll
terribly--then for many people it becomes unfun. You may find it great.
I may find it great, depending on circumstances. But if you want to know why
others don't find it great, well, that's a reason why. I have a player who consistently rolls terribly for damage, and it causes her to check out after a while. She doesn't find it fun to nickle-and-dime her opponents to death.
This is especially true if it prevents the player from running their PC the way they want to. Like, in the 5e game I'm in, Int is my rogue's dump stat (it's a 10, which actually isn't
bad, but it means no stat bonus). I didn't put my Expertise in any Int-based skills--such as Investigation, which is needed to find traps and thus is important for a typical thief. But I'm using the swashbuckler archetype, so it doesn't upset me if I fail a roll to find traps (or to know something about history or arcana or religion or nature); I'm only a rogue because swashbuckler is a rogue archetype (and for that sweet, sweet sneak attack damage). Actually, one of the most fun moments in the game was due to a failed roll to find traps.
But for someone who wanted to play more traditional thief-type rogue who was good at finding traps, then in a roll-under game where finding traps was based on Int, and the rules made them put a bad roll in Int, it
wouldn't be fun.
I'm not sold on the idea that "people like big numbers" when the game tells them that in some cases lower is better.
It's not what the game tells them. It's what their brains tell them. In most non-RPGs, you want a higher number of points. There's relatively few games where you want a lower one. And D&D is many things, but it's not golf.
Consistency of terminology is good as long as the context is also consistent. In 1e, context is everything: if you're talking about a weapon then +3 means a higher number while if you're talking about armour +3 means a lower number.
It could also be written as -3 bonus (where negative numbers are consistently written as bonuses), or something like "bonus of 3" or even "bonus-3", with a note in the beginning saying what that actually means. Like how in many PbtA games, you'll see "hold-2", which is shorthand for "you get to do two things from the following list."