1

Taxi is about 45 mins. and 15 000 Isk. total.
Airport bus is about 1 Hr. and about 2 000 Isk. total : http://www.airportexpress.is/

2

Sorry, the airport express price is per person.

3

Björkur only mentioned one company, the one he mentioned is a bit newer in the airport transfer business and therefore cheaper. Honestly, I have never seen them on arrival at the airport, either the busses waiting or a stand where they sell tickets, but I didn't look specifically. I did however take this company for pickup from the hotel and transfer TO Keflavik airport once last summer 2012... and honestly I won't do it again so soon. My flight was early so it was around 4am and the driver of the minivan was on the telephone the entire time trying to coordinate pickups with a colleague, so we're driving everywhere through the city, often for no reason at all because the colleague had already been there and we ended up waiting at Hlemmur for ages before we could get into another bus. It took much longer than pickup/transfer from the competition. My overall impression: chaotic, uncorrdinated - however, I'm sure they are gaining experience fast.

The standard flybus company that has been doing this for many many years is from Reykjavik Excursions and this is their website.
https://www.flybus.is/flybus?gclid=CL_rmtPQ7rQCFUm-zAodpxYA5A
I've never heard of Hoyt Hotel in Reykjavík, but if you mean Holt the bus will take you right to the hotel. See the website for a list of hotels and guesthouses it will take you to (and pick you up from).
You can buy tickets for this bus after you pick up your luggage and leave the customs area... just turn to the right and you will see a stand marked Flybus/Reykjavik Excursions. You can pay with credit card so no Icelandic currency is necessary. The busses leave every few minutes and you won't have to wait long. Price per person for a one way ticket with hotel drop-off is ISK 2500.

My general opinion: I personally would take the Flybus from Reykjavik Excursions, I find their operations smooth and professional and to me it's not worth the small price difference. I have nothing to do with this company and am not advertising. I fly to and from Iceland numerous times in the year and this is based on my own personal experience.

Good luck and have fun!
mánaljós
http://www.icelandlogbook.blogspot.de/