You are defining income as wages. To be slightly more accurate, the term is ordinary income. I’m defining income as money coming in, whether actual cash balances or unrealised gains. As noted in a separate post, I’m basing my terminology on general financial/accounting terms including those used by Investopedia commentators.
The IRS separates taxable income into two main categories: “ordinary income” and “realized capital gain.” Ordinary income includes earned wages, rental income, and interest income on loans, CDs, and bonds (except for municipal bonds). A realized capital gain is the money from the sale of a capital asset (stock, real estate) at a price higher than the one you paid for it. If your asset goes up in price but you do not sell it, you have not “realized” your capital gain and therefore owe no tax.
And while I’m certainly not going to dig through the US tax code, I’ll note that on Schedule D, the IRS form for calculating capital gains taxes, line 47 identifies capital gains as income.
Tax on all taxable income (including capital gains and qualified dividends).
https://www.irs.gov/pub/irs-pdf/i1040sd.pdf (PDF, p.D-17)
And yes, of course, long-term capital gains are taxed differently than wages, aka ordinary income. As for your third question, I’ve already answered it.
Lower capital gains tax rates are a bit trickier since they’re meant to encourage investment and ultimately increase the amount of tax by having a larger pool of income to tax from. That seems to have worked for when the long-term capital gains rate was set at 20%, but not from when it was changed to 15%. Law of diminishing returns, I expect.