The strip is easily walkable if your lodging is nearby, however, many of the newer hotels are west of the original strip several miles. Most of the hotels in those newer areas will transport you for no cost though. Additionally, the old, original hotels in downtown Vegas are about 3 miles north and worth seeing, but a cab ride would be in order. As far as use of any particular hotels facilities, I've found that they, of course, welcome you with open arms to any of the casinos. The use of pools can be a different matter, though. Some of the pools can be accessed without a key and some can't. Pool side service for meals or drinks is usually only via a room charge, so that would probably dissuade the casual user.
I don't think there are any helicopter flights from Vegas out to the Canyon, since it's quite a distance and the helicopters would be prohibitively expensive. There are several operators of good sight seeing airplane flights though... one of the oldest and safest being
this one . (Go as early in the morning as you can to avoid the turbulence generated by the heat of the day). There are several helicopter tour companies available at the Canyon, an example being
hereThere are many coach tours and the concierge at each hotel can direct you...
Welcome to the U.S. by the way!