If I understand this situation correctly, both red cables are Positive and carry the current from switches. You may want to check both red cables if they really correspond to these 2 switches. If so, I guess You need to choose which circuit (1st red + N + E or 2nd red + N + E) You want to use, cuz I guess You will be using just 1 switch/dimmer (as Your 'new' light needs only 1 Positive cable).
I would check (for safety meanings) red cables (if both run current while switch/dimmer is on), put 1 red to 'A', 1 negative to 'N', 1 earth to 'E' and ISOLATE remaining red cable (using some isolation tape or else). If everything goes well, 1 switch will turn Your 'new' light up and remaining switch would be obsolete.
I'm not sure about all the fixing (if it needs to be done by qualified worker), but I did something like that several times myself.
How do I connect these pin bulbs to the mains - any special holders? transformers, etc?
You can buy G4 sockets with trailing wires, these have mounting holes that can be screwed or bolted, or you could probably glue them in place with a heat-resistant glue. The trailing wires would have to be connected using a 230V connector block.
These sort of parts are available from specialist retailers and distributors (in the UK this would be Maplin, RS, Farnell etc, but there are many equivalents in Germany)
Make sure you buy a 230V lampholder not a 12v lampholder, if it says "halogen" it is probably only rated for 12V.
So far as I know, most G4 usage is for 12V so there is a danger that, now or in future, you or someone else will end up plugging a 12V product into a 230V supply causing failure of the product with a small chance of minor explosion and fire.
What amperage (if needed) should the fuse be?
It depends on local regulations. In the UK the main-panel provides required overcurrent protection to the lighting circuit. If you wanted to provide additional protection I'd add the smallest 230V fuse that exceeds the expected current. But this should be additional to other protections.
The microphone shells are this hard plastic type. Should I do something about insulation so that the plastic does not melt or something?
You should ensure that the bulbs cannot come into contact with the plastic shells and that the shells provide adequate ventilation for the bulbs to prevent overheating.
I'd test the plastic shells with a temperature controlled soldering iron to see what temperature they start to soften at. I'd also take one outside and apply a flame to it for 30s to see if the plastic is the sort that produces thick black toxic smoke and which drops burning molten plastic onto your carpets and furniture setting them alight. At least you can make an informed decision about the risks.
What have I not asked about but probably should?
Most importantly, since you are using 230V bulbs, you must ensure the whole arrangement is safe from an electrical perspective. Usually this means double insulating everything, grounding any exposed metal parts and making sure nothing bad happens when or after your 5 year old daughter/niece/visitor grabs the lowest shell and hangs her weight on it and then tries to put the broken pieces back on the now-broken exposed 230V wiring.
Personally I'd see if it is possible to use a 12V solution with transformer in/at the ceiling.
Best Answer
The electric cooker should have an installation manual. Most electric cookers in the UK are not plugged into a normal 13A wall outlet/socket. They are hardwired to a dual-pole cooker switch on a dedicated cooker circuit (e.g. a dedicated 32A circuit).
A typical cooker instructions will say something similar to this example.
Examples of the required diversity calculations can be found online. For example: https://www.tlc-direct.co.uk/Book/6.5.2.htm
In your photo of your cooker's connectors, the multiple live and neutral connections appear to be each be connected by a copper bus bar. This presumably means that you can attach the supply to any of the screw terminals (brown to an "L", blue to an "N"). Don't use 13A flex or a 13A plug, it'll eventually blow the fuse or catch fire.