Living in the US, after I graduated high school I began attending community college that fall. As I had no marketable skills and a severe disability that made it difficult to get jobs, my parents allowed me to live with them while attending. I got a small stipend from social security due to my disability, and I paid about half of that to my parents. The other half paid for the rest of my living expenses - gas, food (to a point, as my parents did share some things with me), pet food, et cetera. It didn't really leave me a lot of "play money" but that was all right. I knew I had it pretty good. I was expected to help with household chores and so forth even though I was out of the house for at least part of the day five days a week. Three of us split the chores, so it wasn't that bad but it did get a bit tedious. At least, at that time, it was all physical coursework so it's a bit different. Much later after I had moved out my sister and I both attended the same online university where all our coursework, study material, etc was online. My sister had a harder time explaining to her husband and sons that no, she was not goofing off on the computer all the time, she was working. She was also working part time at a fast food place during this period to support the household and pay toward school.
So my advice to you- sit down with your mother, explain that you're frustrated by your attempts to balance all your responsibilities and to manage her understanding of your timetable. However, I don't think you should have to do ALL the chores. Just because you live there doesn't mean you're free labor for your mother and she no longer has to do anything. Work out with her a fair split of duties, hopefully so you're both spending approximately the same amount of time and effort to maintain the house.
I do agree with others that it doesn't take 8 hours a day, five days a week, to look for work online. Break up your job search into blocks of time and work in other duties in between. I realize that you say you have to bike everywhere so it takes you longer to look for work the way your mother is suggesting. Perhaps you can work out something with her there too - "Hey Mom, I want to apply to X Y and Z, they're all pretty close to the grocery store. How about I go with you and drop them off while you're doing the grocery shopping?" "Hey Friend, can you drop me off at Z so I can apply there and I'll make my way home from there?" Even in this day and age there are not many online only jobs, as you no doubt have discovered. Me, I'd love to work from home, but that's not likely - and many of THOSE jobs are perks of jobs you get AFTER you've been working at a physical location for a while. I know you have experience in... underwater basket weaving, but you're not likely to start out with a job dealing with underwater basket weaving. Most of those entry level jobs are still very much 'show up and hand in a paper application' these days. That, and it's a good impression to present yourself well to those you may be working with.