Waypoint, some of these questions are too tough for us! Certainly for me. But here's a try at some of them, it might at least get others to come in and tell me I'm full of it.
2/3. No NDBs are in the data base (they used to be but were taken out five years ago or so) You can manually build an approach, or you can use one with the same ground track (ILS perhaps) and modify it to suit. You can then fly LNAV/VNAV (If your company allows), provided you back it up during the approach by displaying raw data on at least one side of the cockpit.
4. FMS usually has a point one mile from the runway for a non-precision approach, and the altitude equivalent to a normal glide path at this point. It has a label which I can't remember and have not got my manuals to check it, but you will see it when you select a non-prec approach from the data base. It is usually below the MDA, and is handy for vertical track guidance on the ND when you make the last, visual part of the approach. The auto pilot can follow it, but you may not use auto pilot below a point 100 feet lower than the MDA on a non-prec approach. However the vert track display on the ND will show the profile, even if the Missed Approach alt is set in the window.
5. The runway 13L VOR at JFK is flown on a normal profile, descending to 800 feet after the VOR and maintaining that until intercepting the normal descent path to the runway, visually. There is a warning on the chart not to descend too early due to noise abatement. Follow the lights, don't cut the corner, and about half way round the turn (at the second set of lead in lights) you will see the VASIS which is set for a turning approach (if you can see it you can use it). A little anticipation (speed correct, config set, start the power back as the correct glide path is approaching rather than after it is past) and it is a doddle. Aim to be on final track, aligned with the runway, outside one mile. Avoid crossing the threshold while still turning. Just like a visual circuit and a lot of fun, especially with a crosswind (which ATC will always dial in for you). The ILS is never turned on, so don't count on it for guidance. In fact it is best to have it turned off in your NAV page, due to false GPWS warnings on final. When the wind is coming from the north east at more than 20 knots it can give a lot of low level turbulence. The runway is long enough, but go for precision on the touch down, you don't want to float. Most pilots go for a turn off before ZZ so a higher than normal auto brake is a good idea.
For 13R, you simply continue the descent from minima and do not level at 800 feet, and make a continuous turn to final. Very easy.
6. You can use the lower minima for the VOR 25 at LAX if you can identify the point NOELE (4DME or 114RSMO). It does not have to be in the data base. If you are flying with auto pilot then you need to set it in as a waypoint, but with any non-precision approach you are actually using the raw data for deciding when you are at NOELE. In practice, so long as the LNAV/VNAV agree with the raw data, follow the flight director. The non-flying pilot should have raw data displayed and he will call if there is a significant deviation.
Phew.