The output of Series[E^x, {x, 0, 5}] has head SeriesData, but you can get a "regular" arithmetic expression in x by applying Normal:

Normal[Series[E^x, {x, 0, 5}]]

You can feed this to Plot with variable x:

Plot[Evaluate[Normal[Series[E^x, {x, 0, 5}]]], {x, 0, 5}]

I don't know if this is the "best way" for your application, but it is one way.

Your question about displaying things as factorials is an entirely different question (probably should be submitted separately). I'd hesitate to make any suggestions until I knew more about your context, why you want that, and how general the solution needs to be.