Disclaimer: though I have been living all my life in Russia, I am not a lawyer neither a religious person, so I might be not aware of some specific regulations, but I am answering based on my own experience.
I have never heard of any general regulations prohibiting entry to any such chapel or church, so I would see no problem in entering them unless:
- There is any explicit sign outside prohibiting entry, or
- The chapel is on a private area or at least on something that looks like a private area or an area where strangers are not expected. (The one on the left picture can be seen as such, I can imagine some workers emerging from those shacks around and questioning what a stranger is wandering around for. On contrary, for the one on the right, staying in the middle of nowhere, nobody will be asking questions.)
- If you see someone who looks like a local and/or a religious person, you might want to ask them first, though often locals might be surprised at your questions because they would never think that anybody will prohibit entrance.
Obviously, you should follow some more-of-less obvious rules of behaviour around, and especially inside the buildings: be respectful to the place itself and to people around (if any), do not shout loudly, do not take a lot of photos (a couple of them might be OK, or even more if the building is really great, such as Church of the Intercession on the Nerl), etc. Some religious people might say that you must be properly dressed (long trousers and bare head for men, long skirt and some head cover for women, etc), but I think that for such almost abandoned objects this is not too important.
Apart from this, I consider entering such places to be completely OK, and even if you violate some rules, I don't think you will face any serious consequences (unless there is real damage, of course).
As for taking photos, the churches and chapels alone also do not represent any restrictions on what you may photo. Once again, if it is on a private or looking-as-a-private area, some people might question you, but not for taking photos of a church, but for taking photos of them.