depends on what you want the second camera for. if it is just for backup and will not be used very often, then consider a dx camera, your fx lenses will work with a dx camera. the d7100 can be purchased used for a very good price and is an excellent camera, or the d7200 for a little more has a larger buffer if you are shooting action shots with a fast shutter speed. the d7100 or the d7200 will have very similar setup and configuration as the d750
Photomatix Pro. it is easy to use. only problem is you can only load one set of photos at a time, which makes it sort of time consuming if you are needing to do a lot of photos. it can be used as a plug in with lightroom. also, it is more dynamic if you have a few pics with different exposures, but it is not necessary. Photomatix will do a single exposure. also you may use raw or jpeg pics for processing. topaz is another product, but i find it as difficult and frustrating as photoshop.
just backup picasa from the old computer and recover to the new one
if you are only going to use the lens for this trip, consider renting a lens. there are several online services for this, or there may be a store in your location that offers this service. worth checking out.
canon or nikon, it is the same question as chevy or ford. both cameras are excellent for photography. the best way to decide is to see what your friends are using and then use those friends to learn how to use your camera. as for cost, try b&h photo, or some other reputable site, and check out their used equipment. i use nikon and you can usually find a nikon d7100 used for around 500 dollars. it is a great dx camera and you will enjoy it for years. also, when you buy lenses, buy full frame lenses, then when you upgrade sometime in the future, and if you enjoy photography, you will, then you can upgrade to the nikon d750 and you will find that the controls on the two cameras are very similar.
also might want to check out b&h photo. they have lots of used and refurbished lenses and are a reputable dealer. i have never had an issue with them or their products. just go to bhphoto.com
in case you have not discovered it yet, you can set your d750 to shoot at 1.2 or dx 1.5 in the photo shooting menu, then the image area menu. other that that, the d7100 or the d7200 are both great choices for backup cameras. the d7200 has a larger buffer, but the d7100 can be purchased at someplace like b&h photo used for a really low price. whatever choice you make, have fun shooting.
i use a nikon d7100 for a backup to my d750. it works well when i am out shooting landscape. i can put a wide angle lens on my d750 for landscape pics and have a larger zoom lens on my d7100 for when wildlife pics pop up. you can buy a used body from b&h photo or andromada photo for a very reasonable price. it is much quicker to change to a different camera as opposed to changing lenses and i do not lose the shot when some sort of wildlife appears suddenly. if you are hiking, there are camera harnesses that will allow you to carry both cameras compfortably.
i have a nikon d750. it has an option to shoot in 1.2 or dx 1.5. will shooting in these modes allow the magnification of a lens without a teleconverter and achieve the same effect without the loss of an f stop and without losing the auto focus?