The best way of saying it is probably "What's left to do is to clean up the mess" or "All that is left is to clean up the mess."
By adding the "to do" the sentence is given a context which is more useful and grammatically stronger.
By taking away the "," in the second sentence, makes the sentence flow better.
"According to so-and-so" is a well-accepted phrase to indicate a certain level of authority. It doesn't mean authority in the sense of indisputable, world-class, absolute authority. It means authority only at the level of indicating that this is the person to whom the statement can be attributed.
It therefore has rather wide usage, all the way from according to my brother, Nancy went to the dance with Frank, right on up to according to Einstein, the universe is curved.
The lowest level of its reference to authority, however, is the second person, according to you, which sometimes is used sarcastically, thus: According to you, I should never have bought stock in Microsoft. Boy, were you wrong.
We don't take it down to the first person, because that becomes overly emphatic, or to put it another way, redundant. According to me is simply saying, this is what I say. It isn't considered necessary to say this is what I say when you say something. You just say it, don't you? I can tell you Nancy went to the dance with Frank without saying According to me, Nancy went to the dance with Frank, you see?
If we look at your examples, Mari-Lou, we can see a little bit more of why the usage sounds a bit strange to native English speakers. Since we do imbue a bit of authority to the according to locution, we usually feel according to my brother, our father will go to a nursing home someday does sound odd; we would instead tend to say my brother thinks our father will go someday, and the response would be but I don't think so rather than according to me he won't. According to in standard English usage is given some weight of authority, even at the lowest level. It isn't taken as purely opinion.
Best Answer
I think you can get away with it; however, phrasing it like this ("Kelly left an empty spot") implies that Kelly chose to create that spot (maybe not as the main goal, but she knowingly left an empty spot).
When you're talking about a dead person (who did not commit suicide, I guess), I would change the phrasing to:
It removes the implication that Kelly performed the action (leaving a spot by dying).
Minor addition
I think you mean to say
"After she traveled" means that she has stopped travelling when the empty spot is there.
That could be correct (e.g. she chose to stay abroad to live, therefore no longer traveling), but it could also be incorrect (she came back home after her travels).
To avoid confusion, I would say "when she traveled", to point out that the empty spot was only there during Kelly's travels.