Do I report as income ESPP dividends (1099-DIV) if I only purchased stock but haven't sold any?

Yes, you have to report the dividend income even though you didn't sell the stock.  When you don't take the dividends as a distribution, it's re-invested but you still have to report it.  If you don't report it, you may receive a letter from the IRS and they will recalculate your income if you didn't report it.

Refer to the TurboTax Hep articles Where do I enter my 1099-DIV in TurboTax Online? and What Is IRS Form 1099-DIV: Dividends and Distributions? for more information.

Yes.  Stock purchased and owned by you may accrue dividends, which likely accrue in your account.  So you earn additional stock shares through these dividends.  Stock may also pay interest, which would be reported on a 1099-INT form, which also accrue as additional stock in your account.