I haven't addressed leak testing.  There are two types.  One is a visual leak test on the tank and fittings  The other is the distribution system.   (actually there are other tests for the tank but that won't be done in your yard.)

The tank get a visual inspection.  Leak solution (basically soapy water with some additives) is applied to all fittings.  That includes the plug in the bottom of many.  Spray all the connections, remove the dust caps and spray inside, same for the relief valve.  And the regulator.  Be sure to spray the entire flange edge and the vent for the regulator relief valve.

"Pressure test" and "leak test" are technically different procedures.  In the field we tend to use them interchangeably.

At installation before putting it in use a line is supposed to be tested for leaks.  Lines inside a building are to be tested with an inert gas at 1 1/2 times operating pressure or at least 3 PSI.  When a system loses pressure or changes are made in the system it needs a leak test must be performed.

If the tank loses pressure a leak test must be performed AND the service person is supposed to light the pilots.  (That is an insurance thing).  Yes, any time the tank runs out the system must be tested.

Last week I had a customer run out.  Customer owned tank manufactured in 1958.  Filled him up, did a leak test, failed. Shut off the control valve to his space heaters.  held.  Turned on the Ziegler.  Failed.  Turn it off and turned on the Warm Morning.  Failed.  Just to verify before telling him he had to spend money I turned both off and tested.  Failed.  Then I noticed his first stage regulator was making bubbles.  It had not been doing that.  Replaced the first stage regulator and it held.  Everything held.

Leak testing is a good thing