I do not have access to a car and am visiting my soldier's basic training graduation. Can I have a taxi drop me off and just walk on base?

Most cab companies have permission to enter the base. I would highly recommend you contact the local cab company that services the base and see if they can take you to the actual point you need to get to.

Yes, you can. However, Fort Lost in the Woods isn't really pedestrian friendly (from what I can remember). It may be quite a few miles from the gate to the graduation location.

According to the Ft Leonard Wood website you will not need to get a visitor pass if you are a US Citizen on only going to access the base on Graduation day. The required documents to gain access is listed on this page https://home.army.mil/wood/index.php/my-fort/visitors-access . Since you won't have to stop at the visitor center this makes using a cab much easier (and cheaper) The local airport has put together an information paper for those flying in for graduation that has a number of embedded links including one for the taxi companies that are authorized on Ft Leavenworth. It is a good read from someone that has seen a lot of people in your situation. https://www.flyflw.com/services/travel-tips/traveling-to-flw