Let's say I have a car and I want to make some modifications myself without a professional. It can be just for fun or personal research/testing. I may just add a train horn, an auto-braking system, a semi-self-driving system, something like that.
Assuming I don't make a change that clearly and directly makes driving dangerous, like disconnecting the brakes, is it illegal anywhere in Europe to modify one's own vehicle (car, motorbike, etc) like that?
It will very much depend on what you modify. If you only drive on your own land, that's mostly fine (possibly not fine if your own land is a road accessible to the public).
What will cause you problems:
The manufacturer has a general permission to distribute car models with certain characteristics in your country. There's trouble if your modification means your modified car doesn't have these characteristics. Your car insurance is for a certain car model.
Your insurance may be invalid if you modify your car. As "boy racers" were mentioned, part of the insurance cost is based on the type of drivers this car model attracts. If you change it from "boring old family car driven by boring old dads who never have accidents" to "exciting boy racer car driven by maniacs who crash their car regularly", you would be expected to tell your insurance so they can adapt their insurance.
As far as passing your MOT test goes: If you don't advise the tester of the change, and therefore the fact that your car is unsafe is missed, your MOT is not valid. Same in the time between making changes and the next MOT if your changes made the car unsafe. Usually that will be found out at the worst possible time: After you are involved in a costly accident.
To my knowledge, any car modfication that is not simply using manufacturers additions as intended (for example, removing a car seat when it is intended to be removed) is very much illegal until you report the change to your state's vehicle registration office and add the added part's manufacturer's documentation. Even things like new LED headlights (upgrade from old non-led) need to be approved by them. Also car color, window tints, etc. And it's not always easy to get their approval. So my bet would be that yes, it is illegal to do any modifications pretty much anywhere and is quite strictly enforced.
EDIT: As per @NateEldredge comment above, these only apply if you intend to use the car on public roads.
Here's how that works in germany (StZVO §19 -- 22a).
Practically speaking, modifications come in varieties:
Some modifications are covered by the car manufacturer's type approval.
The car manufacturer may sell basic rear mirrors and better ones, say, with mirror with an additional wide angle section. As long as the better mirror is listed as being compatible with that exact make and model (covered by the ABE/type approval), you can just exchange the mirror (step 1 below).
Some potential (expected) modificiations may already be entered in the car's registration papers (incl. CoC).
A van may be sold with front seat row installed but only the attachment points for back seats without the actual back seat rows. Nevertheless, the registration may say "up to 9 seats", and with that you can go and buy the proper back seats and put them in (step 1 below) and be fine.
If that line is missing in the registration papers (saying, e.g., 2 seats), you need to get the registration changed (step 3). This can even be postponed for normal cars (see below).
Some modifications are sold with a type approval for the part. Instructions will tell about the proper installation, and what limitations there are for the use. You add the type approval for the part to your car's papers, and are fine.
An example would be black window foil or car decal which you can put to the car (limitation would e.g. be "not to be put on the front or front side windows"
Some modifications need to be registered, but you don't need to update registration immediately: is is sufficient to do that next time you anyways need to change registration data, see §13 FZV for details on what needs to be registered immediately and what can be postponed.
Example: your car is registered as blue, and you decide to repaint or decal it in red.
Individual modification where it is not immediately clear that no adverse consequences in terms of road safety and emissions (incl. noise) follow, and the type of vehicle is not changed. For this you need individual approval.
This covers everything up to building your own car from scratch. :-)
Here are the steps for individual approval:
modification (you can do that, provided you can and do excercise professional care)
show it to TÜV or similar and get it certified as conformant to all relevant regulation.
This may be a certificate for the individual car, or for an individual part of your car.
In practice, if you want to make extensive or non-standard modifications, you'd want to talk to them beforehand whether the planned modifications can get approval or not.
take the certificate (and possibly show the car again) to the vehicle registration office to get new papers for the car.
tell your insurance
(steps 3 and 4 may be the other way round)
There's EU regulation that says if a modification is legal in any EU country, that applies also to the whole of the EU.
In france, you can make any change you want to a vehicle. But you are not allowed to decide whether the change clearly and directly makes driving dangerous.
Therefore you need to get it controlled by the relevant administration, the DREAL (fr), in order to obtain a certificate of conformity which is required to then get a vehicle registration certificate, needed to drive on public roads.
First and foremost, the EU is not a country. In particular, there are common regulations but cars are still registered in a given country and must follow that country regulations in order to drive in it. For short stays, other countries will almost always honour the registration from other country.
So, the country of registration is relevant for an answer.
In spain all vehicles must be certified for its use in public road, and they also must pass periodic inspections. If you do modify your vehicle in a significant way, you must present it to the relevant authorities (Dirección General de Tráfico) that will evaluate if it is still road-capable.
Cars made by car manufacturers also follow this rule, but that could be less visible because not every single vehicle is revised: they revise just a few vehicles and that serves to certify the whole production.
