2 schools of thoughts on running the day before.
1) rest and save your glycogen stores for race day.
2) warm up and then run a few minutes at race pace. This could look like 10 minutes easy followed by 10 minutes of 30 seconds at 10k pace and 90 seconds jog.
If you tapered the week before, I prefer 2. If you haven't cut back mileage, choose 1. Really don't think you can go wrong with either though.
Eat before? Again, personal preference but choose something easily digestible and that you normally eat. Choose high carb, low protein, low fat. My personal favorite is a whole wheat bagel with a little bit of peanut butter about 2 hours before race time. Less time? Choose a spoon of honey.
If the race is Sunday, too late to truly carbo load. You need a few days before. BUT a pasta dinner the night before would be beneficial provided it isnt loaded with cheese. Besides a carbo load probably isn't needed for a 10k.
Oh and lifting, cross training, core, etc. - definitely skip if this is a goal race. Good luck and let us know what your new PR is!