Note, most ( not all ) brake fluids are brilliant paint strippers, brake fluid is hygroscopic, you will have to look that one up as "homework" , and is effectively killed with water.
Yes, remount the caliper to the fork, to keep it steady. Long extensions are good as they position your hands away from sharp stuff, they also "wind up" so torque can be sustained. You should support an extension so that the socket remains completely onto the bolts hex head, reducing tendancy to ride/slip off, and all the torque, the turning effect, goes into the bolt you are undoing. Rachel's are for quick turn action, not load. Breaker bars are for load. They are long so force X radius equals torque. Same force, longer radius means more torque, the turning effect or "moment".
Sneaky physics and maths and you didn't realise 😎.
Support the extension close to the breaker bar so socket does not ride off, extension stays in line with bolt, and all torque goes into bolt.
Always get Newton to help if you can. Steady torque rather than "jerking". A few please God's also helps.
You know what happens to metals ( usually, metal dependent ) when they are heated ?
Do different metals "change" at the same rate ?
Just look up alluminium and steel for now.
Why have I mentioned hot water ?
Glad that nipple came out all ok.
So, suitably equipped those two 14mm bolts will undo in say 10 seconds each, being generous.
The two pad pins, stainless steel ?
Will they rotate slightly ? Yes ? Good.
I can't quite see in your picture of the caliper if the brake pad cover is off ? Another possible shear off/ chewed screw possibility.
So, the two clamp bolts loose, bleed nipple out. Pads cover, wire clip, pins and both pads ( one has a "shim" ) out, brake hose removed ( mistake ! ), Remove the caliper unit from the forks and strip down. See CMSNL exploded view.
You will be left with a "haudraulic unit" with its piston still in place.
Look on CMSNL to see what is involved with that.
"How do I get the piston out ? " I hear you say.....
Itchy fingers, hare and tortoiuse....you jumped the gun a little but never mind, no damage done.
Come back when caliper unit is stripped down, leaving the caliper piston in for now.
You may realise"if I do this, and then that, it will come out ? ".....yes, think, no gorilla tackticts needed at all, just apply what you know to solve the problem. You will not have to touch the caliper piston at all......
So, come back after unit is stripped down apart from the piston, hygroscopic, wthdtm ! , Metals when hot..........?
Different metals have different....
.......... .
And your thoughts of how to get the piston out without damage or even touching it ?
You have everything needed to do that job in your workspace, or very close by, right under your nose probably......
Hare and tortoise, learn, increase/expand your skills but most of all Enjoy. Dirt washes off.
See you later...
Dd23🎅