Have old ADT system. I want to keep using the system for security fut not for fire. I have a Hard-Wired fire detector that I took off the ceiling to paint. It had been already disconnected and taped off, but now it shows error and goes off on me. How do I permanently disconnect this Hard-Wired detector.

How many wires, what colors, was there a resistor on the detector? If so, it needs to be installed on the loop.

You could install a new detector.
I take it you have Interconnected smokes?
If you positively identify the fire loop at the panel, you could place the resistor there.
May be a diagram in panel to show necessary resistance for fire zone.
If you tell which model, I could tell you the value of the resistor.

The model is the Safewatch Custom.
What do you mean by a "resistor", and how do I set up a "resistor"?

The model is the Safewatch Custom.
What do you mean by a "resistor", and how do I set up a "resistor"?

There are 8 wires - 2 yellow, 1 black, 1 red, 1 brown. 1 orange, 2 blue (slightly different shades of blue).

An "End Of Line Resistor" is used to be sure you have an intact loop(Not Open and Not shorted)/Supervised.
Odd wire colors, you would have to go to the panel and see which of those wires are connected to which terminals, the fire loop should have a resistor across the loop, since you had no trouble before, it was connected to not give a trouble.
Remember how it was?

If you just call ADT, they will walk you though bypass that on the system. It will be a matter of a few buttons to press and then the fire system will no longer function at all.

I have never seen the big companies help past customers at all, even removing their code after Contract is up, to keep the OWNER from using, or to be sure they call them.
May be different up north. The Call Never Hurts(too much).

NO fire alarm zone can be bypassed via a keypad function! What you have is a 4-wire smoke detector (4 wires in and 4 wires to the next detector on the loop.)
If the zone doesn't "see" the end-of-line resistor, you will have a trouble condition on your keypad.
The fact that there are 8 wires at this detector means it is NOT the only fire device on that zone. You must have another smoke or heat detector somewhere.
If you're able to open the main panel, there should be a diagram on the door, indication what value of resistor the zone is looking for. It's been a while since I worked on a Safewatch, but I believe it is either a 1,000 ohm or 2,000 ohm resistor.
If you can locate the last fire device on the zone (it will only have FOUR wires) your resistor will be located there. You can remove the resistor and relocate it into the panel and this will clear your fire zone.
Let me know if you can get the box open and I'll walk you through the process.