You sound like a caring, switched on individual. I think your parents are being unfair to assume simply being in the same house as a 4 year old is good enough - they need interaction with other people, guidance on what to do / what not to do etc - but I appreciate you don't have any control over that.
In terms of some initial practical steps you may want to take (sorry if some seem very obvious):
- Lock any poison / cleaning stuff / medicine in a child-proof cupboard / cabinet. You can buy simple magnetic child proof locks on Amazon. (Don't assume that if it's up high they won't reach it - they'll drag chairs over and put other things on top of the chairs to try and reach what interests them.)
- Make sure the front / back door has a lock (e.g. simple barrel bolt will be fine) that they can't reach - even if they stand on a chair. I always wondered why there was a barrel bolt right at the top of the front door of my flat...then I had a child who could suddenly reach the normal lock and I understood why the previous owner had put one in!
3.) Whenever you cook, make sure the handle is turned away from the edge of the stove / counter, so if the child comes in, they can't pull a hot pan on top of themselves. (The same goes for keeping an eye on electrical cords that may be dangling over the edge of the kitchen counter.)
4.) Talk to your parents again about childcare or even the possibility of hiring a babysitter. You cannot study full time and take care of a young child; and they will need someone to interact with them or they will risk falling behind in their development.
5.) Plan a general routine for them and try to stick to it e.g. wake up, get dressed and have breakfast at the same time each day. Go outside for some fresh air at least once a day. Have lunch at the same time every day. Get into a bedtime routine e.g. dinner, bath, stories, sleep.
6.) Look up the healthcare website / speak to a paediatrician in your area about developmental milestones - this will give you an idea of how the little one needs to be supported in terms of their general health and well being, as well as education.
7.) Don't leave the child alone in the bath.
8.) Will you / your parents be driving them anywhere? If so, you'll need a carseat or booster seat (whatever the legal requirement is in your state).
9.) Will they be bringing any of their things with them e.g. clothes / toys / books? If not, your parents will need to buy the basics. (Are they fully toilet trained? Lots of 4 year olds still wear nappies at night, even if they're toilet trained during the day time. If they need nappies at night, your parents will obviously need to buy those, as well as a waterproof sheet / mattress protector etc.)
I hope it all works out for you and your family.