dumb question. door knob
On most locks, you can often either remove and reset the extension shaft 90 degrees... or they have some other provision for rotating the connecting setup to get the "standard" and normal position for the button.
Yes, vertical is usually unlocked, and horizontal is locked.
With some cheap locks, you are just stuck with what they sell you.
"True eloquence consists in saying all that is necessary, and only that which is."
François Duc de La Rochefoucauld