1. The 0% rate applies to capital gain from all sources, provided your taxable income (including the gain) falls within the applicable limit. The 0% rate applies also to qualified dividends. Note that mutual fund distributions may include qualified dividends and capital gains qualifying for the special rates, but also nonqualified dividends that are not eligible.
2. Roth conversion produces ordinary income, not capital gain, so it is not eligible for the 0% rate.
3. Yes, the annual limit for the 0% rate is indexed for inflation. You can find these limits in the tax brackets pages of our Reference Room.
4. The wash sale rule applies only to losses. If you sell at a gain, that gain will be taxable even if you immediately repurchase identical shares. It doesn’t matter whether the repurchase was at a higher or lower price.