(1) It may seem counterintuitive to some, but my own general policy is, when it comes to little stuff ("how long did it take you to do X"), you just have to trust people, to a certain extent. Sure, some people may blatantly or grossly lie. But most likely these people will reveal their slipperiness in other ways, very very quickly.
Meanwhile -- and I think people are quick to overlook this -- playing the "policeman" role in every transaction with the candidate brings substantial negatives. By definition, it's adversarial. And generally there are (nearly always) non-adversarial ways to get the same information about the candidate ("Are they basically honest?") you're looking for. They take creativity (and an ability to read emotions and pick up on other signals), but they're there.
(2) Much bigger -- really, there's no need to sweat about the time to completion at all. Just look at the quality of the code.
It all just comes down to the fact that everything is interconnected: Good people generally turn out good stuff in reasonable amounts of time. When you're looking at good code, there is, I find, an intrinsic aura of ease and comfort which shines through it -- such that you just can't imagine it took them very long to produce it. Everything just flows -- just like it does when you talk to them.
Mediocre (and dishonest) people, on the other hand... never produce good stuff in virtually any amount of time. Sure, they can take the whole weekend to polish off their code... but it will still look bad, or at best, "Meh".
There might be some false positives (or outright frauds) by this approach), but I suspect very few. And those that do slip through, are easy to spot by other means (such as asking them to talk about their solution, for even a couple of seconds).
As to how likely it is that people will lie, given that we've hired several people who did this homework and they've proven to be as competent as we believed, there's at least some anecdotal evidence that some people have not lied.
You have to ask someone with no skin in the game.
Beyond that, I think "a few hours" is a bit too much to ask for, especially since you are presumably following up with an in person interview centered around the assignment. That's a big time commitment, and the commitment on the assignment especially is very asymmetric.
I'm not a big fan of assignments for this reason. They are just so asymmetric. I've been given interview homework that was supposed to take "about an hour" and it was more like 4 to 5 in reality. It felt like an unreasonable time request. I did the assignment, and did in fact tell them it took considerably longer than their resonates. I was invited for an on-site after all that, but declined for other reasons.