I don't know when the trip to the Tar Pits is, but parking at Farmers Market to get to the Tar Pits, or parking at the Tar Pits to get to Farmers Market/The Grove may not the best plan, unless you really just love walking. They are close if you drive from one to the other, but not necessarily on foot if you are not 100% familiar with the area.
I am a local and I live right down the street from both Farmers Market/The Grove and the Tar Pits/Los Angeles County Museum of Art (LACMA). I know the area well, so I know exactly where I am going and how long it will take me to get there on foot.
LACMA/the Tar Pits are on Wilshire Boulevard, but you can also access them from 6th Street (which is in between Wilshire and 3rd Street).
Farmers Market/The Grove are at the corner of 3rd Street and Fairfax. 3rd Street is north of north of both 6th Street and Wilshire.
You can get a few hours validated parking at Farmers Market or The Grove if you eat at a restaurant in either place - but sometimes it's hard to tell which restaurants/shops actually belong to the Farmers Market part of the property or The Grove part of the property! Some of them look like they belong in The Grove when they actually are part of FM, so be sure you know where you are parking and eating if you go there, hoping to get the free parking.
Now, as for the time it takes to get from Anaheim to the Tar Pits or from the Tar Pits back to Anaheim - yes, it is about 45 minutes without traffic. If you hit heavy traffic - like during rush hour - it could be twice as long as that.
On a Saturday morning there will be a bit of weekend traffic happening, but I still think you should be able to get to the Tar Pits from Anaheim in an hour or and hour and 15 minutes. It won't be as bad as weekday rush hour traffic. I think that leaving at 8:00 would be fine, but allow a bit of extra time if you plan to park at Farmers Market and walk to the Tar Pits from there - you'll definitely need the extra time.
The parking at Farmers Market is almost always crazy any time of day - and it always has been, ever since I was a little girl! - but especially around the lunch hours.
I moved this thread over to the Southern California forum, but I left a redirect so people can find it!