Yes ! Nonstop means just that. The flight goes from point A to point B before stopping.

Direct flights can make multiple stops along the way, but no plane change.

A connecting flight necessitates a stop and plane change. Both flights may be non-stop, but you must change from one to the other. 

Prices vary, but often, non-stops are priced higher. Evaluate each possible choice and combination before choosing. There may be a substantial cost difference.

Frequent flier points awarded may vary, depending on the price.

For long trips, consider a short stop over. Sometimes a break is better than a really long direct or non-stop flight. It's all a matter of personal preference.

Of course, nonstop flights are the fastest way to get to your destination. No stops or transfers mean less chance of delays or cancellations. Nonstop flights also mean less chance  for your baggage to be lost or damaged.

The ticket can only to be used by the person whose name it is issued to. It cannot be used by anyone else except that person.

However, policies do vary among airlines and types of tickets. Always check with the carrier involved to find out what the term "nontransferable" means in their language.

Well gee, I guess that should be very clear (?) However, airlines and their policies are often ambiguous. It should mean that you will not be issued a refund or allowed to re-use the ticket if you don’t use it on the flight it's issued for. Constant changes in policy make it often unclear and open for debate. To be certain, check with the airline in question to determine their exact meaning for that particular ticket.

A few airlines allow nonrefundable tickets to be used another time, sometimes on a standby basis. There is normally a penalty/fee involved to change the original ticket.  When buying from a "consolidator" or "wholesaler",  remember that their agreement with each airline precludes any normal consideration or protection that you might have when dealing directly with the carrier. In that case "nonrefundable" probably means use it, as ticketed, or lose it completely.