As my mother used to say:
If you don't want to be treated like a child, stop acting like one!
And of course the converse is true - if you want people to respect and treat you as an adult you need to demonstrate that you are worthy of this by acting like an adult. In fact that is fundamentally what being and adult is.
One of the key differences between an adult and a child is that they can recognize the need to do things that they might not want to do, or that are unpleasant in the short term in order to achieve a greater overall benefit. Children can't do this - which is why they need parents to make them do these things (otherwise every four year old would be trying to subsist of a diet made up exclusively of ice cream, cookies, and crisps and getting run over every time they came near a road). Parents don't make them eat healthy food and look for traffic to punish them or for the fun of it but because a 4 year old makes it plain with their behavior that they won't do these things on their own.
As you point out, you aren't four any more - and yet your mother is treating you like one. So why do you think that is?
Is it because she wants to punish you, or for the fun of it? Or because you've been acting like one and demonstrating that you're not making sensible choices?
Let's examine each of the two issues you posted about:
Well, by your own admission:
I couldn’t control myself
And you have important-sounding exams coming up. So in this situation was your lack of control in terms of your phone use something a four year old would do? or something an adult would do?
How to ask my mother to cancel the time table for giving up my phone?
It is good that you recognize that it was your actions that lead to the consequences of your parents instituting the restrictive phone policy. So hopefully you should be able to see that logically the way to get the restrictions lifted is again by your actions in removing the impetus for the restrictions.
Show you can be trusted with the phone by demonstrating that you understand why it was a problem before and that you are changing your attitude, do this by studying for your exams (or whatever) and (importantly) don't complain about not having the phone. Once you have done this for a sustained period of time then you can try approaching you parents:
I understand that I wasn't regulating my phone use before - I got caught up in the novelty of it all. However I think I've shown that I can act responsibly and keep my focus on more important things such as my studies. Could we review the phone timetable?
It sounds like you have a skeletal issue (osteoporosis at a guess - given you mention it being Ca tablets and it starting post surgery for a fracture in your spine) which is serious business and believe me, speaking as someone with an incurable, degenerative skeletal condition myself if I could I'd put up with a little bit of daily nausea over the debilitating levels of chronic pain and the steady erosion of my mobility.
You mentioned in comments that you understand that you could experience severe consequences for your health if you stop taking the tablets. Now I understand that taking the tablets isn't great and it makes you feel nauseous but is it really worse than the consequences?
You also mentioned:
I wish I can be like others who don’t need to take pills at all.
Life isn't fair.. and also how do you know who does and doesn't take pills for different conditions? People don't always go around advertising their medical conditions. I currently take two separate medications daily, and I very much doubt a single other person in this building knows about it.
And (assuming the Calcium is to allow you to maintain bone density) how "like others" are you going to feel if you bone density drops to the point where sneezing or laughing breaks a rib or two?
So weigh the downsides of taking the pills versus the downsides of not taking them and ask yourself, what would you rather have?
How to tell my mother that I don’t want to take pills at night, only sometimes?
You don't - because that isn't a reasoned decision, it's the petulant whine of a child. Instead you say:
I'm really struggling with the side-effects of my current pills, I understand that taking them is important for my health so would it be okay if we talk to the doctor or another to see if there's an alternative way to take them without having to deal with the nausea? I'm going to be taking these for a very long time and I think it's worth exploring to see if we can make it easier for me.
And if there isn't a better alternative (I'd be surprised if there weren't though - calcium comes in many forms) then you need to do the adult thing and work out a reason that matters to you as to why you should be taking them. On a question on Space Exploration SE you expressed an aspiration to be an astronaut. Well a big concern for all those in that line of work is Spaceflight Osteopenia where you lose 1% of bone mass per month spent in space so you'd be needing your bones in the best possible condition before you went to space (and I seriously doubt any space agency would accept "I don't want to take my pills because they taste yucky" as a suitable reason to make an exception. Do you? So how about you use that ambition as a reason to keep taking the pills? Even if you have to give yourself a nudge - maybe a picture of the ISS or something in your room that you can look at while you take them to remind yourself of why you're doing it.