They should be ok to add as long as they're not a big percentage of the compost.

You could also add the paper directly to the compost. Shredding first makes paper decompose faster.

You can do that but the nutrient value will be much less than if you by passed the burning and just added the paper to the compost. In the paper making process much of the nutrient value of the resulting paper is removed and the paper has very little of value except the fibers which are carbon and about the same nutrient value as peat moss.

I've read that ash is better applied directly to the garden because its goodness quickly leaches away from the compost pile.

Ash is alkaline---an important consideration.

I wouldn't use ashes directly on my garden because of the alkalinity. Since the OP is from Texas, alkalinity is likely to be a problem there, as well.

The only reason any nutrient value of ash would be leached out of a compost pile is because that compost pile was too wet. Whether the ash would have any nutrient value depends on its source and paper will have very little because all of what is in wood is removed in the pulping process.