I am confused! I am looking to buy a Nikon DX 35mm f/1.8 lens. I have always been under the assumption that 35mm is 35mm...a mild wide angle lens. The exception is an FX lens on a DX camera, where the smaller APS C sensor size, using the central portion of the lens' coverage circle, gives an equivalent angle of view of about 52mm.

I see statements..."35mm is the new 50", and the information printed with the lens description;"52.5mm 35mm equivalent".
I've been of the opinion that nobody that knows anything uses a DX lens on a FX or 35mm film camera, due to extreme vignetting. It seems to me that a 35mm lens, designed for the FX sensor or film should give a 35mm angle of view, while a 35mm lens designed for the APS S sensor should do the same. Where is the error in my understanding?

A few comments:

1) How often are you allowing LR to take a backup? This LR back-up process creates entire copies of the LR catalog and never performs any clean-up of the older back-ups. Consider updating your settings to back-up once a week. Also, go into the Lightroom folder where the LRCAT file is located (typically within your "Pictures" directly). Find the subfolder Backups. Either delete this entire folder, or open and delete every back-up except the most recent date-stamp.

2) All things considered, the LR 'catalog' does not take up that much space. It contains a database of all your edits and 'pointers' to the locations of your images. LR doesn't maintain copies (nor originals) of any of your original image files. So, when you say the 'library' is taking up a lot of space, we're unsure of what you're referencing.

3) Yes, you can maintain your LRCAT catalog on an external drive. To make this move:

3a) Exit the LR software.
3b) Delete the back-ups as memtioned above in item #1.
3c) Connect your external drive and copy the entire "Lightroom" folder from your local computer drive to the external drive.
3d) Rename the existing "Lightroom" folder on the local drive such as "Lightroom-old". This is done to assure you don't confuse yourself that the LRCAT has in fact been moved.
3e) Find the LRCAT file in the Lightroom folder on the external drive. Double-click this file and LR will launch using this file as the new default catalog. Alternatively, start the LR software and when prompted for which Catalog to use, navigate to your external HD. You'll be prompted for a catalog name because you renamed the location in item #3d.
3f) Assure you have a automated or regular back-up process, external to LR, that takes period copies of the entire "Lightroom" folder as now located on your external HD.
3g) Make / take an back-up of the "Lightroom" folder as now located on the external drive, placing that back-up to the cloud or your standard secondary external drive similar to how you backup your pictures from this external drive to still another location.
3h) Delete the "Lightroom-old" folder on your local drive as was the purpose of this exercise to recover diskspace.

4) Regarding the deletion of your edited images, No. The idea of 'library management' or 'digital asset management (DAM)' is to have a library of all your digital images that can be obtained instantaneously. If you add keywords and / or create local groupings of images via Collections, the idea is you can find / identify any image in your library for immediate reuse. This search ability is only as good as your keyword approach, but imagine if you could find every 'flower' picture you've ever taken? Or, find every picture of a specific family member? Or, you purchase a new editing tool and realize you could do a better job on an older image. Wouldn't you want to start from your LR catalog and the existing work rather than starting completely from scratch?