I was kind of hoping for more specific suggestions for ways to incorporate exercise outside of a gym for that first question. It sounds like she’s already pretty bought into the value of exercise, just struggling with specific ways to go about it that don’t come at the expense of her mental health.
I am not in quite the same position — I have never struggled with disordered eating or overexercising, but I do hate gyms, I have no interest in losing weight, and other typical fitness-y goals don’t motivate me at all. So what I do is try to identify what I get out of exercise in terms of how I feel and live my life, then find places in my routines where I can meet those goals. Figure out very concretely, what do you like about exercising? How can you get that feeling/benefit in a low-pressure way, that integrates with things you are already doing?
For example: I like strength training because I like feeling powerful and capable, but I’m mostly interested in how that plays out in tasks in my everyday life, not in how many pounds I can lift, or how many reps I can do. I like to do bodyweight exercises because I can do them in my home without any special equipment, and I can pick from a wide variety of movements. Also a lot of the movements beyond basic pushups and bodyweight squats and stuff are honestly very silly, which I find appealing. I don’t set specific rep or weight goals long-term. Just on a day-to-day basis I will decide things like, while I watch this episode of Gilmore Girls, do sets of these 4 (or 5 or whatever) exercises. Obviously it is not a highly efficient way of becoming much stronger, but it meets my needs and increases the chances I will actually make a workout happen. It’s pretty easy to google lists of bodyweight exercises, and even view videos of the correct forms on youtube, without going into deeper rabbit holes of Fitness Talk.
My other big exercise need is that getting my heart rate up regularly helps me with insomnia and anxiety. I live at the top of a big ridge, so when the weather’s good, a brisk walk down and then up again is a solid half-hour of exercise, intense enough to leave me feeling it at the end but not so much that I can’t just go out in my regular clothes and make it happen at a moment’s notice. When the weather is gross, I have my own elliptical machine, which I do tend to use to do more intense workouts, less often than my walks. Before I bought it, I did a lot of jumping jacks and like, extended solo dance parties to my favorite music. (possibly the reason I hate gyms is because most exercise I actually enjoy is deeply embarrassing to be seen doing.) Again, very little tracking, very little optimization, no “fat-burning zone” or whatever. Just, “have I been getting enough exercise to keep from feeling shitty? yes? great. no? ok, I will do some more.”