I have a large wallet that is many years old.
Before doing anything, make sure you understand what you're doing. People have lost most of their Bitcoin through not understanding change addresses for instance.
I assume you have a cold wallet, don't let your private key touch the internet. Keep it cold.
If you now have all your coins on the same address, you may also want to split your wallet up into different addresses and/or even different wallets. That may make it easier next time you want to sell something.
I want to withdraw something for the first time (about 1 or 2 bitcoin) and sell it on an exchange to pay for my children's studies.
Have you thought about tax implications? Depending on where you live, you may or may not have to pay taxes. Since you're rich in Bitcoin, that shouldn't be a problem. But make sure you can answer their questions once they come knocking.
I want to use a bitcoin mixer to transfer from my old wallet to a new address and from there to an exchange.
If you send 2 Bitcoin from a Bitcoin mixer to an exchange, changes are the exchange is going to ask questions. If you send 2 Bitcoin from an old address, it's obvious you're a long-term holder. But coming from a mixer, they'll be curious about the source of your funds. What are you going to tell them? And how are you going to prove you got them in a honest way?
Once the exchange is happy with your answers and lets you withdraw, your bank will probably ask you where that $85k came from. Again, be prepared to answer their questions.
I need the mixer because I want absolutely nobody to know how much bitcoin I have, not even the exchange. Nobody knows how much bitcoin I hold and I have never told anyone.
The mixer will know! So use Tor and all other precautions.
I have also heard that there are malicious groups that analyze the blockchain and try to link wallets to their real owners to sell this data.
Not only malicious groups, also legal companies do this.
Honestly I'm a bit annoyed that I have one big wallet instead of several small ones but I can’t change it anymore.
What you can do, is make sure you can spend your money legally in the future. Having a pile of money you can't use must be frustrating.
Again depending on where you live, you may not be the first Bitcoin holder who suddenly realizes he's rich, and never reported any of it to taxes. So think carefully about your long-term plan how to enjoy your money.
Finally, I would need an explanation of how to use a Bitcoin Mixer safely.
Sorry, I went outside the box by responding to everything except for your real question
I think the mixing part shouldn't be your first concern.