Pickling Frozen Fish

I have no personal experience, so I can only say what I've found on the web:

There's a guide to pickling fish on the University of Minnesota website:

Pickling is an easy method of preserving fish. Pickled fish must be stored in the refrigerator at no higher than 40° F (refrigerator temperature), and for best flavor must be used within four to six weeks. Only a few species of fish are preserved commercially by pickling, but almost any type of fish may be pickled at home. Refrigerate the fish during all stages of the pickling process.

• Ingredients for Pickled Fish
  • Fish — Use only fresh, high quality fish.
  • Water — Avoid hard water, as it causes off color and flavors.
  • Vinegar — Use distilled, white vinegar with an acetic acid content of at least 5 percent (50 grains means the same thing). This percentage of acetic acid is needed to stop bacterial growth.
  • Salt — Use high grade, pure canning or pickling salt. It does not contain calcium or magnesium compounds which may cause off color and flavors in pickled fish.
  • Spices

(Emphasis added as it relates to your questions)

From the above, it sounds like you've got a good window for pickling, 4-6 weeks, which is much longer than your one week need... though it will likely take a few days for them to get pickled.

As to the frozen fish question, I guess it depends on if you can guarantee your fish is high-quality... the article says to use "high quality fresh fish", which sounds like you might have an issue, though their page that discusses more directly the method of pickling fish, lists freezing them below 0 F (-18 C) as a method to kill tapeworms that may be present in the fish:

Or, if you are pickling raw fish, freeze it at 0° F for 48 hours prior to brining. Either method kills the parasite.

This page from an Alaskan source says that frozen fish is fine as long as it's thawed and they recommend brining to kill parasites.

Before you can properly pickle fish, it must be properly brined to draw out water to firm up the fish and to kill any excess creatures that might be living in the meat. The brining must be done at temperatures below 38 F (3.3 C) for an added measure of safety. This means you can either clear out a large space in your fridge or use the great outdoors of Seward’s Ice Box like we do.

• Ingredients:
  • Fish fillets, defrosted (if using frozen), skin on
  • White vinegar
  • Pickling (non-iodized) salt
  • Water
  • A cool place below 38 F (3.3 C) – fridge or the great outdoors

As to recipe suggestions, that's actually out of our scope of discussion but there are tons of recipes out there on the web including some in the links I've included here.