1. Is there a way I could possibly be able to make myself sit down and absorb information WITHOUT procrastination?
Sit down and start studying. Starting is seriously the hardest bit.
Eliminate all distractions. Do not have your laptop, food, phone or any other distractingthingy in your room. Have everything you need (all materials, resources) near you.
Have a clean and comfortable study space.
If you're not used to studying then it might be better to start off just thirty minutes at a time. During your breaks, don't get out any of the distractingthingy's, maybe get a snack or just do starjumps (sounds retarded but legit works).
2. How do I manage to motivate myself?
If you don't have an aim or a purpose then you won't be able to motivate yourself. Without a goal, there is no motive. Wanting to "go well in these exams" is not specific enough. Set a specific mark/percentage/rank you want to achieve and work accordingly.
Think beyond the now. You do not want to finish the HSC, look back and think to yourself, "What the hell did I accomplish?" or "I could have done so much better" or "I wonder what I could've achieved if I had tried harder."
Ultimately it's your choice. You need a goal to motivate yourself towards, you need to understand WHY you're trying to get good grades. If you don't study, you won't get the marks. So do it.
3. And what's the best way to actually finish studying PROPERLY for these upcoming exams?
I'm not sure what subjects you are undertaking but a good place to start is the syllabus. Look at the, 'students learn about:' list and ask yourself, do I know all of this? Do I have notes on these? Look at the, 'students learn to:' and ask yourself, am I able to do what is asked of me? Whether this be discuss, evaluate, assess, describe etc. If you are short on time then write up summaries and mindmaps.
The best way to gauge how effective your study has been is to do a past paper and get it marked.
I know how you're feeling. It's extremely hard at times isn't it? Hang in there and just keep plodding. You can do this. You're what... 16? 17? 18? Your responsibility/priority right now is to try your best in your studies. All you have to do is sit down with a pen in your hand and move it around a little (or maybe a lot haha). Please do this for both your sake and mine, try to sit down and study, you are a capable and intelligent and complex human being, use this to your advantage! Gogogo.
PRO TIP: Do NOT do what you WANT to do (e.g. watch tv) before what you NEED to do with the mentality that you will "only do this for 5, 10, 15 minutes" because you're fooling yourself. Do what is necessary first.