[b]What are great ways to keep players engaged both IC and OOC?[/b]

Dead easy. I call it A) X, B) Y, or C) Something Else.

Basically, you want players to have wiggle-room to do what they want, but also to not make them feel burdened to drive your game on their own. Every time there is a natural break in the action, give your players two options for how they want to progress, while leaving options open for them to come up with their own ideas.

A) Explore
B) Have a fight scene
C) Open offer to do something else

This way, if people like your own ideas (A and B), they'll say so. If they don't, they'll suggest something for C. This gives players options for how they want to progress without railroading them or without overburdening them to drive your game without support.

The other key thing is: don't leave player characters unattended - otherwise, you're only leaving them with Option C. When a game first starts, each intro post is each player finding their feet. If they intend to engage other characters (which is normally where an RP succeeds or fails in my experience), [i]facilitate this[/i]. RPing is [i]communal storytelling[/i]. If you leave (most) players to tell the story on their own, they'll run out of steam and leave. Or, at least, I will.

Basically, players should feel like they have something to contribute in their own way. This means constantly leaving strands [i]obviously[/i] open for them to pursue, if they so choose - which means constantly leaving them things to pursue, while not being tied to any one arc.

Never [b]ever[/b] adopt the sandbox mentality. If your players wanted to drive a game, they'd GM their own.

[b]Should the character submission be the only factor in accepting players?[/b]

No. The key thing for me is [i]getting[/i] a game. If you [i]get[/i] a game, but submit a character that won't work, the GM can explain to you why they don't work and what would work instead. If you don't [i]get[/i] the game - you never will, either because it's not the game for you, or because the GM isn't presenting it clearly enough.

[b]How do you deal with the players who have seemingly disappeared from the RP?[/b]

Shit happens. Honestly, it does. Make no character indispensable and pre-build in your strategy for removing each character from the game if it comes to it. You can't force people to stay.

[b]In the same vein, how do you effectively prevent the above from hindering your other players?[/b]

Prepare for the worst - hope for the best. See above. If push comes to shove, the forum would probably be happy for you to Godmode to keep things swimming along.

[b]What is the most graceful way to end your RP due to inactivity or (*gasp!*) your own loss of interest/time?[/b]

By being honest. If you don't have time for it, you don't have time for it. The best you can do is hope people don't hold grudges, but, if they do, it's because their own life isn't as complicated as yours, so they're lucky to have the time to be bitter. 

[b]Surprise![/b]
The single magic bullet that I would recommend is a good OoC atmosphere, one which allows for idle chatter as much as actual OoC discussion. The idle chatter keeps people liking each other and involved at least at a checking-in level, while the latter keeps people giving a shit about the plot and their characters - if they lose interest in their own characters, they simply won't write for them any more (and thereby withdraw from the game).

[b]MUGCoD[/b]

This stands for Mass Unguided Conversation of Doom, which, in my experience, is the kiss of death, and to be avoided at all costs. Never leave more than three characters alone without having some plot planned to disrupt the action. RPing is super-flawed in that it's basically impossible for Player Characters to have natural conversations without planning them before writing, and the more characters you have involved in a given interaction, the messier it tends to become. If you don't have an end-goal to any given interaction in mind, you're relying on 3+ players to all maintain roughly the same level of activity and for at least one of them to have the confidence to draw that scene to a close.

[b]Tl;dr[/b]

Keep players engaged. You do this by fostering a chatty OoC atmosphere and an IC where each character has the freedom to contribute their own thing.