English questions

Kill them. It's the only language they understand.

More seriously, 'look it over' is the only correct answer. It's quite possible that people who say that you can use either haven't really given much consideration to the matter. For one thing, they don't strike me as the sort of people who might consider that the input of others is crucial -- which explains the problem.

I suppose the reason that I didn't answer kizolk's original question was that I felt that there was no real reason to be dogmatic about it, although his instinct as to what sounded better was reasonable.

I would say "I'm done cleaning" and "I'm done cleaning up" are two valid phrases with different meanings, at least as I'd use them. "Cleaning up" refers to a more targeted cleaning operation (e.g. "After dinner, it was time to clean up"). But in general if you're just taking about a large-scale dusting, organizing, etc. of a living space, I'd just use "clean," like "I've spent all day cleaning in preparation for our guests to arrive." You could also say "cleaning up" in that context, but I think I'd interpret that as a bit more focused on de-cluttering rather than mopping, stain removal, etc. And when used absolutely, I also might use "packing" without its particle, with a similar distinction ("packing up" would refer to a more targeted act of putting away some sort of temporary display/structure, like "After seven hours of displaying my wares at the farmer's market, it was time to pack up and go home" vs. "It took me a long time to pack for my upcoming vacation"). 

Now to answer the actual question, I'm not actually sure; certainly if they have a direct object it would sound weird (e.g. "I'm taking my shoes off and calling this wedding off" could not become "I'm taking my shoes and calling this wedding off," not that that's a particularly natural example either way). In your sentence, I'd say that "I'm done cleaning and packing up" sounds more natural than "I'm done cleaning up and packing up," but not because the particle is being carried over to both verbs; I'd just take it as the absolute usage of "cleaning."

Let me add that I find phrasal verbs to be one of the biggest difficulties in learning/speaking English. I feel like they're an essential thing to master in order to sound natural, especially in casual/slangy speech, but they're so many of them (and sometimes easy to confuse) and like you showed, they can differ quite subtly from their non-phrasal counterparts.

This lack of mastery is something I've noticed in the English of many Francophones, and I'm guessing that the same said could be said about foreigners in general.

I think I like the quoted version best actually. I just find it disturbing when a plural verb follows a singular noun, collective or not, even though I probably do it once in a while.

To me it makes the litter sound like one composite entity with a single soul or something along those lines. It sounds mysterious, maybe even sinister. Like it could be a litter of hellish animals controlled by a devil spirit. (OK, I guess that's just my poetic side speaking.)

I am Legion Litter