1. Magnet.
The magnet is stuck to a metallic spacer that is supposed to be glued to the antenna base. I re-glued it and reapplied the adhesive paper: it seems it holds better now.
2. Length.
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3. Testing.
First on-air test was positive as I could hit the repeater from the underground garage, which is not possible with the UV-82 stock antenna.
Second test was on the road. I could see the antenna through the glass roof and it is stable even on bumpy asphalt at 60 km/h. Signal reports from the usual friends were positive as they know how I got through every morning with the rubber duckie.
Third test at high speed. The antenna is positioned above my head and I can see it through the glass roof. My car has no flat metallic surface, so the small base does not touch 100%. At 117 km/h the antenna begins to vibrate: probably a bit faster and something bad happens. I can try to fix this with a small spacer that reduces the front-back empty space, but that's low priority considering that I rarely drive out of town and speak on the radio.
Fourth test at "DX" distance. This surprised me most. I could hit my usual repeater from far away, through a valley where I could do the same with a 20W mobile RTX and a better performing antenna (theoretically).
So after all I will keep this antenna and enjoy mobile HAMming. But I had to modify it to suit my needs and safety requirements.
Now I do want to check the SWR.