Definitely do LOTS of practice papers or questions. Get more comfortable with them and try to manage your time as efficiently as possible. It's tough in the beginning, but as you do more and more, it will get easier and you will inevitably improve
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Practice the multiple choice tests without any time limit at first, try to understand the questions. You will notice that there are common types of questions for example, in verbal reasoning, there are usually questions like 'no acorns are octopi, some octopi are unicorns, all unicorns are eels, which of the following is true?' For this, you would do something like draw venn diagrams and although it was hard at first for me, it became easier and saved me more time because I did so much of these questions. If you need to guess, correct me if I'm wrong, but it was statistically proven that guessing one letter (C,C,C) rather than random letters (A,D,B) will improve your chances of getting the questions correct. Only do that IF you have no idea what the answer is and purely need to guess. Otherwise, the process of elimination is very useful.
As for the writing tests, I guess the best way to improve is by writing a lot. Post it here on the ATARNotes forums and maybe the others or myself will try to help out. You should aim to complete it in 15 minutes or less but go overboard a bit if you have to, because you will eventually improve. For the analytical essays, the structure should usually be an introduction, three body paragraphs (one rebuttal) and a conclusion. Try to be clear and straight to the point. For creative pieces, make sure you use all the senses (sight, touch, hearing, taste, smell).
Tutors are not necessary if you can put in the effort yourself. Yes, they can provide you with more resources and advice, but I think you can get that or something similar from ATARNotes!
Melbourne High wants 'more than just marks'. Try to participate in lots of extra curricular activities (like debating, leadership and such). It's what they're looking for in students and will help you stand out during the selection process.
In terms of the resources, I mainly did practice papers (from Spectrum Tuition) but also online as well. I can't remember the websites I used but you could have a look at this one:
https://www.indiabix.com/Best of luck in your endeavours and remember that it's definitely possible to get in, but only if you want to put in the time and hard work!