How late? If you are talking up to about 9pm. It wont be a problem getting your visa, and you wont need to download it before you go, plenty at the airport - just make sure your 1 of the first off the plane and you'll be through customs real quick , the worst it has taken me is 20 minutes.
Yes, they are fairly safe but you must distinguish them from the touts, My Kenyan wife use 2 or 3 taxi drivers on a regular basis, once I'm in nairobi again I'll post a couple of mobile numbers for you, - somewhere round the 2nd or 3rd of Jan if they agree. No more than Ksh1200 is what you should pay.
yes, you can get the hotel to book it for you but then you will pay through the nose for it - in dollars, o one will have any change and the hotel gets a cut of the drivers fee, book one direct and let him have al the money with no hotel commisson - better for his family.