You are asking very though questions
While solderdure has given you the correct and analytical answers, let me attempt to give you a more laid back one.
Almost every headphone changes the tone of the sound they are supposed to reproduce, e.g. they produce some frequencies "louder" and some "quieter", which effects tone of what you are hearing. A mid bass heavy headphone might sound like a teenager kid lowering his voice pitch to impress the girls for example - you get what he is saying, but that is not how he normally sounds. Equalization is used to correct for that change introduced by the headphone, so that you can hear what it is supposed to sound like, and therefore you would normally have one set of EQ settings for one headphone.
People do measure how headphones change the tonality of the sound and share EQ settings for them, which you can find online and use. Most of them work really well if you use a reliable source, but by no means you have to follow exactly what you find online - you can also play around and see what you like. You can also have multiple EQ settings for different types of genres , unless you NEED them to sound "correct" that is of course (funny, writers, painters, sculptors would leave some of the meaning to the interpretation of the beholder, but for some reason, that is not the case with musicians and recording engineers - they get very upset if you don't stick to their intentions
)
Yes, you can use EQ to add bass to a headphone. You would most likely be limited by distortion in that case, that is, add too much bass and it starts sounding weird, even less
bassy at times. In my experience, a headphone is much more than just a Frequency Response curve some people here would like you to believe though. Will the headphone seal properly on your head, for example, is an important question to ask for a closed back headphone because if the cans are very sensitive to seal, and your glasses are breaking it for example, than say goodbye to your bass. solderdude talks about these in his reviews in good detail actually, recommend you to check those. Maybe there are some other reviewers who do as well - I don't know.
If you are getting serious with this hobby, my recommendation to you would be to get yourself a Quedelix 5K, which has a nice EQ function you can control from your phone, and go out to the store and try a bunch of headphones with and without EQ, increase / decrease bass, see what you like. Once you understand your own preferences better, it becomes much easier to get a sense for what you might and might not like, and don't worry about the price tags too much (i.e.. expensive is not always better, and not everyone
needs a 1000HP car in their lives)