How to check completeness of a bought set?
You've already discovered yourself two good ways:


count by ten
put elements on large surface by type


The latter technique can be extended to an art called "knolling":


Place all elements by type in right lines with right angles on a large surface...
Its a very relaxing exercise and fun in its own right. Checking completeness becomes trivial, building afterwards can also be done with much less frustration.

Update: Here's another very impressive knolling. The UCS Millenium Falcon 75192 
 (7541 pieces) https://i.redd.it/q51wrtua5yb41.jpg 
(can't insert picture here directly since too large)