No, I mean, how does he physically do it if the corresponding muscles are paralyzed?
I wouldn't know, but since his condition exists in reality, it's not unrealistic.
I always figured that they gave him liquid or other soft food that he could easily suck in with a straw. I'm not that aware of this condition, but it could be that he's still able to relieve himself. Maybe it's just his arms and legs (and vocal chordes) that are paralyzed and everything else still works?
Automatically. A lot of systems (like the heart, diaphragm, throat, and bowels) work independently from the brain, and it typically requires training one's mind explicitly to overcome these systems in order to have any semblance of control over them. Noirtier eats and defecates because if he couldn't, either he would have died of heart failure long ago or nothing with a body too large to absorb sufficient air through osmosis would have ever come into being, or failing that, consistently died a much more disgusting death shortly after every single birth. Presumably, his servants take care to be certain he doesn't choke (such as feeding him a diet of liquified food and punching him in the chest every time something goes down the wrong pipe).
In what is essentially a decades-long morality play, it's always bothered me that the most moral character in the book winds up paying for crimes she never committed. Mercedes is the only person of her generation not to have intentionally harmed anyone, and yet she winds up broken and alone, while Dantes sails off into the blue horizon with a hot young thing. I know the book is of its time, but the other female characters seem to end up with fates that align with their actions. Why is Mercedes so screwed?
YMMV seriously on whether Mercedes deserved it or not. I don't neecessarily say she deserved to be alone, but arguably Dantes might have been less harsh on her if she hadn't married Ferdinand Mondego of all people. If she had waited a decent interval, say a year, and married someone for comfort and security and maybe a little love, I think things would have changed a lot - but she married her enemy and was too naive to think any deeper into it.
I don't think Ferdinand Mondego was her enemy. He was Dantes' enemy, to the point where they only shake hands because Mercedes tells them to. But to Mercedes, he was always a friend, and she knew that he loved her, she even loved him back in her own way - just not nearly as much as she had loved Dantes.
I don't think it was intended to be a "punishment." If anything, it's a testament to her character, in that she's easily able to give up all the things Fernand provided for her upon learning of his crimes against Edmond and settle down for the life she was "meant" to have in Marseille. Even if she would have him, that's a life Edmond would never be able to go back to.
The count specifically tells her that she should not have given up all the wealth that Fernand had amassed, because part of it was hers by right. He actually intended for Albert and Mercedes to live in peace and relative comfort after he was done with Fernand. Mercedes becoming a hermit and Albert joining the African army were entirely self-inflicted punishments.
When playing as Busoni in front of Caderousse, Dantes condemns her as an unfaithful woman for marrying so quickly after he disappeared, and the implication seems to be that she probably never should have married at all (since he wouldn't have been happy with any amount of waiting). It's possible that Dumas agreed with this sentiment.
As I recall, isn't there some implication that she was aware of her husband's crimes, or a least knew where not to look and what not to ask?
Madame Danglars gets the short end of the stick as well, considering there's nothing particularly "bad" about her character, besides being somewhat neglectful of her daughter. Villefort is the one who buried her child alive, while it's shown that she was unaware of this and is still stricken with guilt over the whole thing. She cheats on her husband, certainly, but it's shown over and over that Danglars is a horrible and domineering husband, and doesn't even care about her unfaithfulness. She even found a way to become financially independent! Yet she ends up dishonored and in fits of hysterics. Even Eugenie is last seen with her head bowed in shame, despite being able to run away with Louise.