The magnet shows gentle attraction in the area of the yellow circle, and stronger attraction in the area of the red circle. What can I do about this?
I can't see your red circle.
You can Copy and Paste pictures into your post.
It's quite likely that you have a sediment blockage in the pipe, that is preventing the radiators being topped up. This has probably led to insufficient water in the system to circulate, it has air in the top part. That's why water did not squirt out when you tried to bleed the highest radiator in the house. The blockage will have existed long before you saw the fault.
The brown mud is iron oxide, basically rust, from the insides of the steel radiators. Inside the pipes it may be black, and sometimes very hard. As an iron compound it is attracted to a magnet (the black more so than the brown)
If the blockage is in the bend (likely) then the blocked section has to be cut out and replaced with new; or scraped clean and replaced.
Before starting any more work, tie up the ball float in the feed and expansion tank, bale it out into a bucket and remove the water and all the mud. Otherwise more of it may find its way into the pipes, and also squirt out over you when you cut the blocked pipe. Sponge the tank, and lid, and float, clean, and wipe them over with bleach to prevent fungus or bacterial growth in the short term (don't pour it into the tank).
Then look for the main system drain cock, as the whole system should be drained and cleaned to remove residual sediment, or it may block again.
If you are not fond of DIY plumbing, ask around for a local plumber or heating engineer, by personal recommendation from someone whose opinion you value. The fault is very common and any tradesman will have done lots of them.
Website searches are not a good source as the business will usually have paid to be listed, and in some cases can censor unfavourable customer comments.
This pipe is not part of the boiler and is not a gas or combustion part so a plumber can do it who is not a gasman. This might be cheaper, if it matters to you. I know a semi-retired installer who does little jobs like this.
If you have to get a powerflush it will cost you £hundreds, so if you want to save a bit, a DIY clean is worth a try. You will need a cleaning chemical, which is not expensive, and some time.
I am a DIY-ing householder, Ian is a professional and has done lots more of these.