Hows the weather condition In South Dakota around March??? Is it possible to drive from Chicago to South Dakota around this time? Are parks going to be open?

According to

www.nps.gov/moru/planyourvisit/hours.htm

Mount Rushmore is open all year. For other attractions (and there are dozens), you'll have to look up each one.

March in the upper midwest is variable -- you could get an early thaw and have temps in 60s F, or a late blizzard and fight to drive to the parking lot. It being SO early in the year, it should be no problem to find lodging. Just be flexible in what you plan to see, and base it on the weather that occurs.

Some of the Custer State park roads, Needles Hwy, Iron Mt. Road, will still be closed for the winter. But the main highways to Mt. Rushmore like 44, 16, 385 will be fine, unless there is new snowfall or a blizzard.