What do you mean by “save” as in “copy the file to the encrypted container” or “open the file in a picture editor and saving it”? The former won’t re-encode, the latter likely will.
Renaming a file won’t change its content and therefore won’t change its format.
If the pictures are important to you, make sure they’re backed up appropriately. For even remotely critical data, the rule of thumb is 3 copies across two different mediums with at least one copy at a different location.
Re-encoding MP3s will also degrade quality. Storing them in a ZIP file won’t re-encode them though.
Transcoding an MP3 to m4a will degrade its quality too. The opposite is also true; if you’re downloading music from Youtube for instance (M4A, OGG), don’t convert it to MP3.
The discriminator here is whether lossy compression is applied which is distinct from lossless compression. As the name implies, it loses information in the process.
JPG, MP3, M4A, OGG and many other common formats use lossy compression.
ZIP and PNG use lossless compression; files added to a ZIP file can always be turned to the exact same files again from an encoding standpoint.