Sports Day effect..?

We will be around Kanazawa on October 13 Sports Day. What will be the likely effects?
e.g.can we hire a car and get around ok, will things be closed or crowded?

Traffic on national holidays is usually lighter than on weekedays, but tourist spots and shopping districts are much busier than during the week.

Nevertheless, I don't think you should encounter any major problems. Only the finding of parking near tourist spots could be a challenge.

During the Sports Day Holiday on a Monday in October, will tourist sites such as temples, castles, shrines, and gardens (that require an entrance fee) be open on that day?? How about the following day, Tuesday?

will tourist sites such as temples, castles, shrines, and gardens (that require an entrance fee) be open on that day??

Yes!

How about the following day, Tuesday?

It depends on the individual attraction. Many museums, for example, are usually closed on Mondays, but move the closing day to Tuesday when a public holiday falls on a Monday.

Temples, shrines, castles and gardens, usually do not have closing days, at all.