Will it ever be possible to take a photo inside a nucleus, at the level of quarks?

In my opinion, no. At least in the sense of ordinary human notion of seeing. When speaking about objects, smaller than the wavelength of visible light the ordinary notion to see becomes obscured. The structure of objects smaller, that the distances of order $simeq 500 $ nm, is determined by scattering of more energetic objects or field ion miscroscope.

As for nucleons, there are not someting static, like some balls, orbiting and colliding with each other. It is rapidly evolving substance without a notion of shape and size (except for some localization length).

You need extraordinarily high-energy fundamental particles to see that small directly. Typically when we hit a proton or neutron with that much energy, it fragments and new particles are created, shooting off in various directions. Direct images are out of the question. The best we can do is calculate backwards from the debris to figure what must have been there in the first place.

On that basis we reckon that the three quarks take up a stable triangular shape, holding it together with a cloud of virtual gluons.

Whether the original victim was a neutron or a proton must likewise be calculated from the charge and/or parity of the various pieces of debris.

No, and here is why.

To resolve a small object (i.e., make a "picture" of it) requires a light beam with a wavelength significantly smaller than the physical dimensions of the object. Because the hadron is tiny and what's inside it is even tinier, you need an extremely short wavelength to resolve it in any kind of detail- shorter than that of any beam of light.

Since a particle like an electron has a wavelength which decreases as its energy increases, you can use a beam of extremely energetic electrons to "illuminate" a single proton, and by measuring the angles through which the incident electrons get scattered after hitting the proton, you can deduce the "shape" or mass distribution of the interior of the proton. This is what Mr. Rennie calls the parton distribution function.

This "snapshot" isn't the same thing as "taking a picture" of the insides of a proton, but physics dictates that this is the best we can do along these lines.