Use your own body weight to strength train. Planks work the entire body. Press ups, tricep dips, crunches, lunges and squats, clams, pelvic lifts and calf raises. I've picked 4 of these a day to compete and I'm about to start rotating different exercises each day.
Yoga is a safe solution as well as Zumba if you would like something more fun! In YouTube you can find classes according to your level. I have done also ballet classes should you prefer something like that.
YouTube has a ton of great videos (Jillian Michael's is particularly tough). Because of COVID19, Peloton is offering a free 3 month subscription and they have a pile of strength and cardio exercises that range from bodyweight to heavy weights. Good luck!
Yes, but how you do it depends on whether you have weights or not. If you dont have free weights or exercise bands, I would look into that. Exercise bands take up very little room. If you have neither, then use your body for the resistance. Pushups, chinups, lunges, squats, and tricep dips using a chair are all good. I would recommend looking at different websites to find one that explains the exercise so you are using proper form.
I like to do a lot of body weight and endurance exercises, if you do squats and nothing but squats for a whole song trust me your legs will be burning. Also YouTube is a great resource for whatever level of fitness you're at of at home workouts. I really like Yoga by Adrienne