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Seaweed is actually quite nutritious for plants. In addition to using seaweed extract, if you are near the coast at all (or know someone that is), you could also try harvesting some seaweed and composting it for your garden. Here is more information on that: https://www.gardeningknowhow.com/composting/ingredients/composting-seaweed.htm

If it is a clumping type of kitty litter, I would not use it in the garden due to the chemicals in it. If it is a normal clay-based kitty litter, it can go into the garden, but it will not dry up areas. Do not add it to sandy soil. This will harden the soil and damage it.

Yes, a mix of those 3 items will provide the main nutrients plants need and should work well.

Here is an article that you may find helpful: https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/how-to-improve-clay-soil.htm

It is hard to say as they are influences by many factors. In general, powdered lime will leech out of the soil fast than pelletized. Powdered lime will work faster, but the amount of time it woks faster is small, almost nothing really.

Here is an article that you may find helpful: https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/how-to-improve-clay-soil.htm