you can make Traditional IRA or Roth contributions for prior tax year up until the tax filing deadline, April 15th (allowing time to determine MAGI limits etc). When you make the contribution at your brokerage you need to designate which tax year it applies for.
conversions are different, you mentioned both in your question. Conversions from Trad IRA to Roth can be done any time but apply to the calendar year in which they are done they cannot be backdated to a prior tax year.
