My self-employment lasted only for part of the year, e.g. Jan-Jul '21 - do I enter car expenses only for 7 months or the entire year?

You would report either the business mileage you had when in business or the expenses you had while in business. 

Thanks @Bsch4477! So I assume that the denominator for mileage would also be just the total miles I drove in the first 7 months, e.g. in the first 7 months, I drove a total of 4,000 miles, 800 for business = 20% use for business; for 2021 a total of 8,000 miles = 10% for business. I ran my business as a sole proprietor and thus there are some expenses where it would be better to claim the whole year and some (like the car) where it would be beneficial to only claim the time where I was actively self-employed. Do I have the choice?

You have the choice of deducting your actual business mileage at 56 cents per mile or using your actual expenses multiplied by the percentage of business use for the 7 months.