yes

It's about 30 miles away and takes just under an hour so you'd need transport. If you have a hire car – no problem. There are tours that'll take you there some also factor in a stop off either coming from or going to the airport.

You can use the same bus transport and take it either to the BSI busterminal which is about 10-15 minutes or you can take it to bus stop nr. 8 which is by Hallgrimskirkja, just 2 minutes walk from the hotel.

Yes, you have to pay taxes for staying in this Hotel. As I remember, it is substantial amount, the same taxes as all hotels in Iceland.

We stayed here last year at the end of September, and our room had two balconies. (FYI they are narrow). One faced the church and the other had an amazing view of Reykjavik (see photos in my review of the hotel). I think it was a junior suite with balcony. I must say the large and spacious room was awesome. As far as the balcony goes, although the views were awesome, at the time of year, we did not put much use to them because it was cold. We actually used the balcony to chill some drinks! Lol I would say it really depends how much time you’re planning to spend in the hotel room, and what your budget is. If you’re willing to splurge, it is worth it for the spacious windows and opportunity to step out into the fresh Icelandic air! But if you’re looking to save, the balcony doesn’t get you much more. It’s more valuable to walk the city and explore. Hope this helps!