1. If you are a single income household it is always better to file jointly, unless you are trying to keep assets separate. If you file jointly the upper limit of the 15% tax bracket is ~75k. It's only ~37.5k if you are filing separately. The former makes your idea much easier to execute.
2. Kinda. First, taxable income, not AGI, is the metric you should track. This is great, because Taxable Income is way easier to keep low than AGI. Not only will your 401k/HSA/IRA reduce it, but so will all of your deductions and credits. Mortgage interest, college expenses, moving expenses, child tax credit... All of these things will help keep your taxable income below the ~75k threshold that is the upper limit for the 15% tax bracket (married filing jointly).
3. You should make sure what you are selling is long term capital gains. Depending on the fees of your funds, it may be better to wait to sell a portion until next year, if the income from these sales will put you over 75k in total taxable income.
4. Unless you are already pushing 120k or more, or don't have a mortgage, I don't think you'll have a problem getting below 75k.