can you bike on the trails?

There is a trail of about 1.5 miles through the woods around the perimeter of the garden. If you want both gardens and a hike, Tower Hill would be a good choice. If you're just looking for a hike, get the AllTrails app

Orchid show

No

Probably not, they're meant for meandering

I don't know, but I doubt that you could as they wind around the flower beds and would have many people walking particularly on weekend days.