Four days is an extremely short trip, but the price is good. I was toying with that yesterday, even though we leave for Iceland yet again tomorrow, lol.
1--Do not drive trying to look for the aurora. You do not want to be driving I the pitch dark on unfamiliar roads that are very narrow and have no shoulders and no street lights. Either just look up wherever you are, or take a tour. You can actually see them a fair amount fro right in the heart of Reykjavik believe it or not. One the best shows we have seen was from there. If you take a tour, I highly recommend Aurora Experts. We have used him a few times and cannot speak highly enough of him.
2--The commercial and rustic hot springs are both great. We like a mix of them on each trip. Blue Lagoon is the most famous of course, but Sky is really nice and is right in Reykjavik. GeoSea is up north and you won't have time for that with just 4 days. Hvammsvik is my favorite commercial one hands down, and you could do it and combining it with Snaefellsness makes the most sense. Don't forget the local pools in town.
3--Katla is the year round cave, and we have done it but in the winter. At the end of September it is just before the rest f them start, for safety, so I would either choose Katla or use the time for something else.
4--No, IME the sheep roundup is not worth chasing. The locations are all over, and to find the exact timing is like looking for a needle in a haystack. Don't worry, as you drive along you will see farmers rounding up their sheep along side the road, so just be careful as you drive and give them space.
5--The south coast is beautiful, but so is Snaefellsness. You won't have time for both. With flying in from SEA (same as us) that first day is best spent in Reykjavik itself to get over jetlag. Then venture out the next morning. You do want to be closer in to Reykjavik/Keflavik your last night in case bad weather closes roads, etc. I am comfortable staying as far as Selfoss, but would not stay any further away. Since you love the high waterfalls, I would suggest the south coast. Snaefellsness has a few high ones, but its draw is basically the diversity and it is alike a mini Iceland. The south coast would make the most sense for what you want with your limited time. As for hiking, if you have any doubt about Glymur, then yes it probably is not for you. There are plenty of other hikes around that are easier and take less time, again making the most of the time you have.
6--Don't worry at all about communicating. Everyone speaks English and as long as you are polite, you will receive that back.
Definitely do not stay in Reykjavik the entire time. Do that the first night and then you have almost 3 full days. I would suggest either of these. One, a night in Vik, a night in the Golden Circle and the last night on Snaefellsness. The other one would be to skip Snaefellsenss and add that night on to Vik so you could do a day trip up to Jokulsarlon.
One thing to note, you absolutely need to be at the airport a good 3 hours before departure. Security doesn't take very long normally, but passport control can be an absolute nightmare. We have had too many flights there that we barely made it. This is now what we do and it works well. When you arrive at KEF, you will see self check in kiosks against the outside wall. Check in there and self tag any checked luggage. Then go towards the desks that will be empty, and just on the left side of those is where you scan your tagged luggage and sent it away on the conveyor belt. Then you will go upstairs to security which will then dump you out into the duty free store and the area with shops/restaurants. There are toilets here as well. Do not sit and hang out in here except for maybe a quick meal. Do not wait for the gate announcement here. They do not announce those until about 45 minutes before, which means passport control becomes absolutely a zoo.