The best thing to do is have a look at eBird, THE best resource for planning trips to Iceland.
Úlfljótsvatn is ideal for seeing Barrow‘s Goldeneye in winter, they should be easy enough on the lake, particularly at the northern end of the lake
https://ebird.org/hotspot/L1284289 and between the dams
https://ebird.org/hotspot/L1154353.
Harlequins are on the coast in winter, usually easy to see here
https://ebird.org/hotspot/L1487215 or even from the bridge over the river here. Also easy further along the coast near Grindavík
https://ebird.org/hotspot/L1312736. They can also sometimes be seen nearer to your base at Þorlákshöfn, generally outside the harbor where it is a bit rougher.
No King Eiders reported in SW Iceland (more common Feb-April) but any large flock of Common Eider could potentially have one.
Gyr Falcons occur anywhere in that area, but it’s just a matter of luck. I saw two from my window at work in Reykjavík yesterday but you could also spend a couple of days searching and not see one! In winter there are often big numbers of gulls and wildfowl on the river in Selfoss here
https://ebird.org/hotspot/L2315056 and Gyr Falcons are frequently seen on this area (Gyr Falcons are hidden on eBird so don’t appear on the list of species on that link). Coastal areas and harbours are generally the best bet otherwise.
Keep your eye on this page, safetravel.is, as we frequently have weather you don’t get in the UK and have had several very severe storms recently (including yesterday and today) where travel by road is severely restricted or not possible (temporarily). Don’t panic, just be aware that winter travel in Iceland can be very “adventurous.”