Hail All! 
Well...I'm already glad that I started this thread - We've got some very interesting problem-solving approaches coming up already! 8)
Roosters don't lay eggs so there is no egg to roll.
Correct! As
Roosters are male Chickens, they can't lay eggs at all - Unless they've become the victims of a rather sick GMO experiment!

If the Chicken in question had specifically been a
Hen, then there would've been a nice egg to make an Omlette with! :razz:
Q: If it takes 3 men 2 hours to dig a hole, how long will it take 1 man to dig half a hole?
Making the assumption that "half a hole" is a hole that is 50% the size of the original, then it would take one man about three hours to dig it. However - This being a trick questions thread - My answer is automatically incorrect.
So what I'll suggest insted is that it takes this one man one hour to dig the hole...As he is doing the work using a JCB, whereas the other crew of three were all using manual shovels! 8)
Alternatively, it takes the one man
no time at all...The hole has already been dug by the crew of three people mentioned in the original question!
Where was the man when he fell off the cliff?
Either:...
- He'd have started off at the top of the cliff dangerously close to the edge, and finished up at the bottom - Splattered all over the earth in a most horrific, satisfying manner!
or...
- The man in question is gay, and Cliff is his boyfriend/husband. After falling off, he ended up back on the bed lying next to Cliff!

The times in my question are irrelevant, for all it matters it could be two separate occasions at any time during the day. I've not included any time in travelling to the machine or waiting for it to heat up (this isn't required). I also have a tray so don't have to make multiple trips
I'm near enough completely foxed by this one, although I bet I'll be kicking myself at my stupidity when the answer is finally revealed!
Just to have another hack at it:
The crux of the riddle could be in the
kind of drinks that ye are obtaining, and what each person requests...

Say that when ye started the day, ye went to the machine and got a black coffee, a white tea, a hot chocolate and a cup of tomato soup. Each drink would've required a seperate instance of operating the machine (Inserting your KlixKey, selecting required drink, waiting for drink to be prepared, and taking said drink) which would be 30 seconds per drink.
However...When ye go to the machine later in the day, the requested drinks are two cups of white coffee and four cups of plain water. The machine - Being capable of accepting requests for multiple drinks of the same type at once - Would make the two cups of coffee in about 40 seconds, and four cups of tapwater would be three seconds apiece - A total time of 52 seconds to obtain six
drinks! 8)
Farewell...
>> Death <<