luckyphil55 1. Can you have secure mobile phone turned on to receive messages and calls, and be my answering machine when I am unavailable and not be located at the same time? Or are all mobile sims tracked when on?
It's not the sims that are tracked, but the cellular modem in your phone if it's on. If we simplify a bit it looks roughly like this: when you turn on your phone your modem scans for available networks and connects to nearby cell tower(s) even if you don't have a SIM card. This is why you can call emergency services even if you have no reception from your network, because you're connected to some other provider's cell tower. If the tower happens to have your network, your SIM card serves as your login and password for it, so it authorizes you and you can make calls. The point with tracking is when your operator receives a call for you they must know to what exact cell tower to route it in order to reach you. Hence they must know where you are. It's by design.
As for mitigation, the only way is to enable airplane mode and only then turn on any antennas you need, e.g. WiFi for internet access and GPS for navigation. But at this point you won't have working cellular connection at all, so your calls and texts won't work. You could try using a VoIP service that routes your cellular calls via regular internet (kinda like Signal or WhatsApp). A good example of such service is jmp.chat. You could purchase a number there for a test and later port yours to them and use it as you normally would if you like the service. The only difference is that under the hood the calls will go through the internet network rather than through cellular one. For it to work you'll need to install their app called Cheogram. You'll be receiving calls/texts through it when your phone has internet access. If you're offline or won't answer the call, you'll receive a voice mail message which will be transcribed and sent to you along with the voice file if you prefer to listen for it. If you're interested, give their FAQ section a read. Keep in mind, this whole thing works only when your phone is online. So if you'd like to minimize cellular tracking and continue to be reachable, you'll need constant WiFi connection. There's no other way.
luckyphil55 2. Is there an "unlocated" map ap I can have turned on and not be located?
Yes, apps like Organic maps, Osmand, Magic earth will help you with this. You can download maps ahead of time and then go completely offline, e.g. enable airplane mode, then turn on GPS only. GPS works only as a receiver (like FM radio), it doesn't send anything anywhere.
luckyphil55 3. The three cats Pixel 9 does way more than I think I need but is it a good local starting point?
Pixel 9 is a great starting point and will be supported for many years.
luckyphil55 4. anything else I need to research?
Give GrapheneOS website a good read if you haven't and come back with questions.