The dress code is formal.
The ceremony is outdoor in the garden area (weather permitting). Cocktail hour is indoor/outdoor (there is indoor seating, but you can also enjoy the patio area). The reception is indoors, but easy access to the patio if you want.
Yes, there is a bus that will pick up at both the Doubletree and Hyatt House hotels. This section will be updated when the pickup times are confirmed.
You can take an Uber/Lyft. If you are coming from NYC, It can be expensive to take an Uber/Lyft into NJ depending on time of day and how busy it is, so one option is to take the PATH train from Manhattan to Grove Street (on the Newark bound train) and take Uber/Lyft from there. https://www.panynj.gov/path/en/schedules-maps.html