If I sell some stocks shortly after I buy them ( like in 30 days), I get short term capital gain which is taxed at higher rate compared to stocks one sells after keeping more than a year. If I sell stocks in both categories, but short term stocks have more gain/income than stocks I held more than a year, Would I be taxed for all My income at a higher rate or Are there any other factors or things I can use to lighten my tax burden?

Qualified dividends and long term capital gains are taxed at either 0 or 15% depending on your other income. See the worksheet.

No matter how much your other income your tax on QD or LTCG can be no more than 15%.