I have spent more than a month in Iceland in the winter so here are some responses to your questions based on my experience:
1) Road conditions depend entirely on the weather forecast. Unless there is a major winter storm when you visit, the roads should be in good condition. The roads in the places you are visiting are plowed frequently but do expect some snow and ice. The Icelandic road administration has an excellent website with road condition information that is regularly updated. It is an essential planning tool for winter travel in Iceland.
2) We used a guide named Oskar from Ice Guides for a private ice cave tour that included about 2.5 hours in the cave. Even tours for photographers do not give you much time in the cave and you will be surrounded by many other photographers. We had a really good experience with Oskar and his price was not much more than the group tours. If you do go with a group tour, they book well in advance so make reservations early. I would not recommend going on a group tour unless it is specifically for photographers or you will likely be very disappointed.
3) Iceland's meteorological service puts out an aurora forecast each day. That is a good place to start. The University of Alaska has good resources on their website for both short and long-term forecasts as well. You can get a sense of whether or not the aurora might be visible in the general location where you will be but the forecasts are not specific enough to know exactly what conditions might look like in a specific spot. And, even if the forecast is for a good display, you still might not see anything.
Most of the places you are visiting have become quite popular with photographers so do not expect to be alone (for example, we have seen about 75 photographers at Jokulsarlon at night for photographing the aurora) in February.
5) An SUV is a good option but be prepared for it to be pricey. 4-wheel drive will help with driving on snow and ice, as the roads can become treacherous in bad weather conditions (especially once you add in Iceland's notorious wind). There are smaller rental companies that rent full-size SUVs which might be a good idea if you are worried about driving on ice and snow. Smaller SUVs with all-wheel drive or 4-wheel drive will also be adequate if you plan on staying on well-traveled roads and are comfortable driving on snow and ice. We have rented a campervan from Happy Campers twice in the winter in Iceland and that has also been a good option (much easier for chasing the aurora and being close to some of the best photo locations like Jokulsarlon).
My husband and I have written a comprehensive guide to photographing Iceland, which you can find in the ebooks section of our website (linked in my profile). We provide a lot more detail related to some of your questions in the ebook and offer a lot of location ideas.
Have a great trip!