On a PC, think of it this way, iTunes and Apple Music are one and the same. iTunes can be called a program or application, it doesn't matter. iTunes is the program/application you use on a PC running Windows to access your Apple Music subscription.
First Thing:
With an Apple Music subscription you essentially get unlimited free downloads of any music in the Apple library for as long as you maintain your monthly Apple Music subscription. The "catch" is that you LEASE that music from Apple - you don't own it. If or when you cancel your subscription, all that music will go away. You can't convert any of the songs to another format (like MP3) or burn it to a CD. See:
Add and download music from Apple Music or buy music from the iTunes Store - Apple Support
As the above link says you can also BUY music (you buy each song or album individually) and download it from the iTunes Store (with or without an Apple Music subscription). In that case, you OWN the music you bought and can do whatever you want with it for as long as you like. If, for some reason, you delete it on your PC you can redownload it at any time. See the "How to redownload music on iTunes for Windows" section in:
Redownload apps, music, movies, TV shows, and books - Apple Support
Second Thing:
What you are asking is very convoluted. What do you want to listen to your music on? I assumed it was just your PC since you said you are not interested in your spreading music over all your devices. If so, then I'll restate my first point - AM & iTunes are the same thing on a PC. If you want to listen on other Apple devices, then you can easily do it with a an Apple Music subscription (for music you LEASE or OWN) for as long as you subscribe by syncing all (or some) of those devices. See:
Turn on Sync Library with Apple Music - Apple Support
Otherwise, for music you OWN, you can sync your iTunes library to other Apple devices by following these steps:
Use iTunes to sync your iPhone, iPad, or iPod with your computer - Apple Support
And, in this case, you can covert them (for non-Apple devices) and/or burn them to a CD:
Create CDs and DVDs in iTunes on PC - Apple Support
I'm not sure how to answer your questions about playlists & searching since iTunes & AM are the same thing on a PC. iTunes is just a program/application for accessing your Apple Music subscription on a PC. Given that, you should be able to sort playlists and do searches.
Intro to playlists in iTunes on PC - Apple Support
If that is still unclear, feel free to ask again.
