To find a nice place for solo travelers in rishikesh is actually easy, the city has a lot of hostels Blue Jay, Mustache, Backpacker panda, Zostel these are all nice hostels and if you'll follow the streets around zostel you'll find tons of hostels or even cheaper stays
Best time to visit ooty is in between april to june and October and November but i made a trip to ooty in February and it was great and less crowded for more information checkout my travel story of ooty
As per state guidelines, no requirement of covid-19 reports for people...so, travel freely, but responsibly...(there are many places which are miles away from nearby roads and hospitals...dont be the reason of spreading virus at such places where medical emergencies cant b addressed immediately....)