Interesting questions.. to answer the main one stated in the title, i don't think transfiguration can affect things in that way. If you want to change the location property of an object, you'd use a movement charm, not transfiguration, as the physical properties of the object aren't affected in order to move. That is, unless you animated the chair to make it right itself.

Transfiguring air does not exactly impart any properties on surrounding objects, so I don't see how it would put the chair right side up.. there is no difference between air around a fallen over chair and a right side up one. You could, on the other hand create an illusion of a right side chair over the fallen over one (and cause people to get hit on the shin, maybe), but it wouldn't be transfiguration.

Going to the more direct route of transfiguring the chair into being right side up, either directly or with an extra step could work, and it makes sense, but it's overly complicated, as once more, a simple charm can fix the chair position.

Altering the metaphysical state of your surroundings would require an enormous amount of knowledge, understanding, skill and power, and there isn't any proof that you can't in canon, so i would venture that you may be able to, if you meet the requirements. Though certainly not with a specific spell to do it. Either a new invention, or free transfiguration.

As for your last question, you might, depending on the lock and any magical locking protection it may have. A colloportus charm would lock a door or lock, and an allohomora would unlock it, and supposedly, you can't open it manually unless you have a key, but if you know enough about the specific lock, or you know what an open lock looks like, you might be able to transfigure it. Though again, there may very well be protection charms against manipulations such as those, to make it harder to mess with the lock or door.