Are low charisma characters...unlikeable?
I decided to simplify this question because you were asking to many things at once and it was going to force me down all sorts of tangents.
Not to put to fine a point on it, but, yes, low charisma characters are unlikeable. That is a pretty large portion of what low charisma means. It isn't everything there is to charisma primarily because 'like' is such a weak and generic word and charisma is such a broad one, but we certainly wouldn't expect low charisma to mean ordinarly 'likeable'.
Of course, not being likeable does not mean everyone will dislike you. Some people may not judge you primarily on your charisma. Some people will like you because they are the sort of people that likes people despite their flaws, and perhaps in some cases you might find yourself liked because of your flaws. Sometimes you'll just get lucky and say the right thing at the right time and make a friend who thereafter is inclined to overlook your basic unlikeability for the sake of your friendship. But, yes, playing a low charisma character certainly implies someone that is unlikeable.
It is plain and simple bad roleplay to have a low charisma character and not signal it in someway through your play. That ought to be obvious.
I can't help but notice the double standard going on here.
Suppose I introduced an NPC and played him as very likeable, attractive, congenial, persuasive, and even magnetic (and a couple of times I've even been told by players I successful pulled that off, which was very flattering considering how unlike myself it is). Then suppose latter you discovered that said NPC had a 4 CHR. You'd almost certainly think to yourself, "What the heck?!?!? Why did the DM stat out a character as having 4 CHR, if he was going to play it as a character with above average charisma? The DM's actions taken together make no sense. He has every right to introduce a high charisma NPC and stat it out, but if he was going to do so, why didn't he just give the NPC a high charisma?" Likewise, if I introduced a character who I played as a cunning mastermind always one step ahead of the players, you'd probably find it ludicrous that I gave the character a 5 INT. How I had played the character did not reflect the stats of the character and did not signal to you anything about the mechanics of that character. I ignored the character's attributes.
Now, in most cases that would just prompt raised eyebrows, but there are circumstances I could do that as DM where the player would have cause to accuse me of - if not cheating exactly - then at least not being a good DM. As DM I have a massive amount of knowledge about, well, everything, and particularly I have a tremendous insight into the tactics, abilities, and defences of the player's characters and into the actions and preparations undertaken by the character's. I'm effectively omniscient. Generally speaking however, it is the understanding of the character's that I won't use my out of game knowledge against them. That is to say, as DM I could play every creature - whether ooze, zombie, wolf, or orc soldier - as having perfect knowledge of the players feats, remaining hitpoints, armor class, combat abilities, magical buffs, and everything else, so that in every situation every monster finds itself in, I as DM always make the strongest and most cunning tactical plan I can thing of using all the knowledge in my possession. But of course, I don't do that, and if I did do that any group of player's I've ever encountered would not be amused at all (I know I wouldn't be). As a DM, I expected to play the character and keep my out of game knowledge from influencing how I play the NPC's as much as possible. If the PC's cast a fire resistance spell over the whole party before facing the red dragon, then I shouldn't have the dragon avoid using its breath weapon. If the PC's storm the castle through the sewers, the castle defenders shouldn't have anticipated this move and put all of their defenses there unless the defenders reasonably could have anticipated the move. And so forth.
In short, I suspect alot of you are demanding that the DM be constrained by RP demands in ways that you are claiming the PC never should be.