You should study the entropy of black holes.

No. Photons can carry information & are massless.

"Information" only exists if a cogent perceptor registers an event and encodes it in an electrical synaptic storage medium (or other method heretofore unknown by humanity). That storage medium has mass.

Maybe. https://phys.org/news/2022-03-state-universe.html#:~:text=Melvin%20Vopson%20has%20already%20published,the%20way%20humans%20have%20DNA. This guy's hypothesis is that it does, and he's got an experiment to see if he's right

It’s very philosophical premise. What is information and how do we manifest it? Eg the data in disc doesn’t “occupy” anything. Empty disk means mini magnets pointing random directions and “data” means they are arranged certain way. Nothing gets added or removed. Then - does magnetic field interact with gravitational field, that’s different type of a question.

Dr. Melvin Vopson of the University of Portsmouth, in the UK, has a hypothesis he calls the mass-energy-information equivalence. It states that information is the fundamental building block of the universe, and it has mass. This accounts for the missing mass within galaxies, thus eliminating the hypothesis of dark matter entirely. https://bigthink.com/hard-science/dark-matter-theory/

Which weighs more, “000000111111” or “100011101100” - that gives you your answer

If the information is encoded with energy, for example, puts the system into a more energetic state, then I guess it will have mass, since energy has mass. That's as deep as my understanding go's though.

Bekenstein's bound can be interpreted as a minimal energy to store information in a given region of space. It's been proven theoretically. And, since energy is mass... In order to have experimental proof, I'm pretty sure we would need to tinker with black holes so... We're not there yet. In any case, it doesn't mean a full hard drive is heavier than a formated one. It's not.

Ask @neildegrassetyson