Description states item weight is 1 pound and shipping weight is less than 1 ounce. So what is the actual weight of lead i am purchasing?

Package says tape is 1/4" X 72" and a 4" strip weighs about one gram. So if my math is correct the total weight of the tape in one package is about .635 ounces. Hope this helps

What's the thickness of the tape? I know it's 1/4" wide but what's the thickness, or depth... need it for a non tennis application.

Using machinist's digital calipers I estimated the lead tape thickness (with the protective paper cover removed) in the range 0.0065 to 0.0075 inch (0.165 to 0.191 mm). There is an adhesive layer on the tape itself that may have increased the readings slightly. There also appeared to be some variation in tape thickness along its length. Lead is quite malleable causing the tape to wrinkle from handling giving a variance in readings and lowed readings if compressed by the calipers.

With the weight of a few grams, will it have such a noticeable effect on the racquet?

It depends on where you place the weights. 3 & 9 should give you more stability. At 12 it will give you little more swing mass.

Is there an index on the package showing how much tape equals how many grams. For example 1 inch might equal 1 G. Don't know

No, It doesn't tell you how much lead equals grams. But it does explain where to place the tape to keep the same balance in the racket. I've added the tape three times (one on top of the other) to come as close as I can to the weight I want in my racket.