Quod Libet can do 1 and 3 for sure, I think it can do #2 but I'm not positive. I don't have a music collection with very many albums that have multiple tracks. You can pick and choose which metadata columns show up for your library and sort by whatever you want, including creating your own but that's outside my expertise. It can do bulk renaming too.

I was using Clementine for awhile, then because of a lack of updates and some other minor issues, I switched to Strawberry which is a fork of Clementine. It added some neat features but lost a few too. After using a dozen or so different players, I found Quod Libet just works like I want it to.

The way I listen to music is to dump all my files into a single folder called "music", then do shuffle, repeat all. I was in the process of moving my files to a new storage and moved the folder around a few times. Just had to update the library with a scan, took like 10 seconds.

I also have it set up to automatically resume playing from where it left off. One of the options is then queue autosave interval, which does the resume from where you left off. It's enabled by default I believe. You can set it to autosave every second if you want but to use less system resources, I stick with the default of 60 and I think it saves on shutdown/restart too. I've never noticed it NOT resume from where I left off.

It has a plugin system to add features but otherwise it starts off very bare bones. You add plugins to basically build your own player the way you want it. That means it can be a bit of work to initially setup. While that sounds like a pain, the amount of time I've spent in Quod Libet's settings is a tiny fraction of the amount of time I spent messing with Clementine and Strawberry's options, as well as other players. It's probably the music player I've seen the GUI for the least in my entire life, as a ratio to how much music I've listened to with it.