What problems could I expect from 750 li with 100000 miles

Not many with that car. . With proper maintenance it will go double that and more, much more. Read your owners manual to be sure you are doing what BMW recommends at that interval.

At that mileage if it has a rubber timing belt(s) could be a good idea to change out. If that baby lets go could be big $.

Sometimes the 100,000 mile service can be costly on some cars. People will trade the car in on a new car instead of spending the money which can be more than 10% of the car's value. Find out what service has been done and apply the upcoming service in your negotiations.

At a 100k you are going to start having some issues. Some issues are not that expensive, but others can be. Headlight modules tends to go up, transmission slippage, the starter and alternator problems.

I have a BMW 750li what I should do with it

Give it to me. I will take good care of it.

I am thinking of buying a 2013 750Li with 1,016 miles very good condition should I get it?

Only 1,000 miles? If this is true it should be like brand freakn' new. What is the story on this car?