If you are dropping somebody off, and on your way to another pick up (or intentionally going to busy area), yes, those miles are deductible.
Yes, you can use the Standard Mileage Rate.
You should be keeping a daily log of your miles. Your Uber log probably shows the time you drop somebody off and pick up the next person. If there is only a short period of time between them, the IRS shouldn't have any problem with understanding that those 'extra' miles are for business.
