I am looking for a word for "the ability of being interacted to/with", expressing that something is interactive, its interactive nature/quality. Specifically looking for a noun.
Interactivity which refers to something being designed to respond to the actions, commands, etc., of a user.
You might prefer
Usability which refers to something having serviceability - that is, the quality of being able to provide good service
Depending on the specific context (who/what is doing the interacting?), you might be looking for "interface".
Symbiosis comes pretty close. It's a mutually beneficial (or harmful) relationship in which each part interacts with the other part in give-and-take fashion. I supply what you need, and vice versa.
Then there's reciprocity or reciprocation. That's an interaction in tit-for-tat fashion. You paid for my meal today; I pay for your meal next week. Or it could mean simply, "I push; you pull."
How about the Spanish word simpatico? If you and Juan get along well together and you interact well with each other, you're said to be simpatico.
I'm not too crazy about mutuality, but it's a possibility.
Complementarity is pretty close to interactivity, as is compatibility. Put two "opposites" together (e.g., a saver and a spender), and once each one recognizes the strength in the other, they can have a marriage made in heaven.
On the other hand, a person who is interactive by nature is
Then there's miscibility, which is a word from chemistry, but I suppose it could function metaphorically as well. Both chemicals and people can interact in various ways, as in an admixture of oil and water and soap (the oil and the water do not interact, but with the addition of soap there's an emulsion, as the result of the soap's interaction with both the oil and the water), or as in an admixture of personalities, temperaments, styles, modi operandi.
Am I on the right track?