Can a married person open a personal Roth IRA? If yes then is contribution limit based on last year?

Yes, this is called a spousal IRA. Assuming the couple is filing jointly, the total MAGI of $170k is below the Roth income limit, so each of them can contribute $6k to a Roth IRA despite one spouse not having income.

The 2020 MAGI determines the limit for 2020 Roth contributions, including those made by April 15, 2021. However, contributions designated for 2021 (which can be made from January 1, 2021, through April 15, 2022) depend on the 2021 MAGI.

from multiple comments you made:

But I don't know how much I will make in 2021. I may guess approximately. Say I guess I will make 170,000 in 2021. I contribute 6,000. Then I get lucky and make 1 million in 2021. Then what happens? The 6,000. That I contributed in 2021 becomes illegal?

One of the great benefits of the IRA or Roth IRA is that if you are concerned about the limits, you can wait until the year is done and then in the January 1st to April 15th period decide how much to contribute, and to the type of contribution.

One could say that by doing it this way you are missing out on a potential year of growth. But by doing it this way the worry about exceeding a limit is reduced.

Some people wait until the early 2021 period to make their 2020 contribution, and they use the tax refund to fund the contribution. Yes they can determine how much they will contribute, and what type of account hey will contribute to, include it on the tax forms they submit in February or March, then when they get the refund a few weeks later put the money into the IRA/Roth IRA. They just have to beat the 15 April deadline.

Also if you do contribute more than you are allowed, it isn't a crime, as long as you address it on your tax forms and move the funds be the required date. There are many questions about how to address the excess contribution. It will cost you money in terms of taxes, but you won't go to jail over it.

IRA's are individual, that is what the I stands for. There are provisions regarding limits (minimum and maximum) when people are married. Those provisions can determine how much is deductible, and how much can be contributed. But there are no joint IRAs.