You have no "gain" on stock A until it is sold. When you file your tax return, you only report gains and losses from stocks that were sold, so in your case, only the loss from stock B. Losses are limited to $3,000 per year, as you stated, for as many years as it takes to bring the loss to zero. However, gains and losses are netted so if you were to sell a stock for a gain, that could offset any loss and "use it up."

A pitcher throws the ball to home plate and the umpire just stands there. The batter asks - "Is it a strike or a ball"? The umpire says "It ain't nothin' til I say what it is. Well, in the stock market your stock ain't nothing until you sell it. The current "price" or "value" is 100% irrelevant to anything.

You are correct on both issues.

you take the gain or loss upon the sale of the security. it makes nada difference if you are holding a loss or holding a gain. in the case you describe, you take the full loss, as it less than $3000 (irs.gov)

In one calendar year:

I buy stock A and stock B.

Stock A: $6000 gain, but still holding it (Held for more than 1 year).

Stock B: $2000 loss, sold it (held for 2 months).

When I file my taxes, would I claim the $2000 loss from stock B, I sold, and not report anything about stock A since I have not sold it yet!?

I know there is a limit on claims for stock loss I think $3000 a year, unlimited years until all loses are recovered? is that true?

Thanks!