Bolt thread size or wrench size?

Usually, but not always the stem bolts that tighten onto the steerer tube are a 5mm wrench size, thread size 6mm.  But there may be exceptions out there.

The bolts on my Deda Zero stem are M5 by 16mm. AK is 4mm. I think the bolt heads, albeit tapered,  would be classed as socket head. Spare matching bolts for various Deda stems are available eg from Condor Cycles.

Brilliant, Andre. Have you thought of writing as a career!?  🤣

I'm curious to know if a used Brooks saddle have to be replaced by a new one..

If yes, how can we know ?

There's a tensioning bolt under the nose of the Brooks saddle. You take a one-eighth turn on it when the saddle starts looking hollow (the proper English is swaybacked -- don't ask me why: English isn't my first language, by half a dozen or so, so I would have said that if we have to have a horsey metaphor it should be lordosis, an equine spine symptom). In your case maybe a quarter-turn. When you've used up all the thread on adjustment bolt, you take the bolt to a welder and ask him to weld on a longer piece of threaded rod, same diameter and thread count per inch. If you're worried about the appearance of your clearly neglected saddle, buy some neat foot oil from your local saddlery (more £$%^&* horses), pour the contents of the can into a baking dish or a bowl large enough to take the saddle and soak first the top and then bottom in the neat foot oil, 10-20 minutes per side. You do that only once, then a thin layer of Proofide once a year only on top. After the short soak in neat foot oil lay the saddle aside for a few days to dry out a bit, then polish only the top with a soft cloth. Tension with your longer bolt and you're good to go for several more years.

A Brooks saddle is like a Catholic wife, you marry it for life, no divorce.