Is there a shuttle bus to take you from one attraction to the next? Thank you.

Yes, and it is FREE! There are a handful of spots but the main three are just outside of the Max station elevator nearest the zoo, Hoyt Arboretum and the Gardens which is near both the Portland Japanese Garden and the Rose Garden. It runs year-round daily May-Oct and Weekends Nov- March.  http://explorewashingtonpark.org/getting-here/#

Yes. There are shuttle busses that run about every 15 minutes in a loop

I m not sure .

Yes. There are shuttle services.

I was there for a day and I couldn't find it

Yes there is!