New to Unity, trouble with physics it seems!

Your objects are falling because you've attached a Rigidbody component and gravity is turned on by default in a Rigidbody component. You can:

• Turn gravity off in the Rigidbody component of each object

• Turn on the Rigidbody.isKinematic flag in the Rigidbody of each object

• Disable or turn off the Rigidbody component for each object

• Create a plane below your object for them to rest on (the object must start completely above the plane for this to work).

Raise your player position in the y axis by about one meter.

Sounds like you don't have a collider on your terrain, objects, or both. Go through your terrain and objects and see if they have a collider assigned to them in the inspector. If they don't, scroll down to add component in the inspector -> physics -> then a collider of your choice. Have fun, mate!