To answer your questions:
Besides, how do I start the case studies, and can I do it by myself?
I always recommend candidates start out by learning what the case interview actually is. You can read an intro book like Case Interview Secrets or Case In Point, look at guides here on PrepLounge or company websites, and watch videos of experts doing a case. Once you’ve understood the basics of a case interview (structuring an answer, some common frameworks, case maths, etc.), I suggest diving into live case practice, where you do mock case interviews with a friend, case partner, or coach. There’s really no substitute for live case practice – this is the most important part of case study preparation.
So, you can do the initial learning part by yourself, as well as some drills on weak points once you’ve done a substantial number of cases. However, for the bulk of case prep you will need to work with a case partner or coach.
Honestly, I don't have any former internship experience, I did research, volunteer and part-time jobs. Is it possible to secure a graduate role next year at any T2 or T3 firms in consulting? Such as EY Parthenon?
It’s hard to give advice on this in such general terms – I’d need to see your resume to help determine how competitive your candidacy would be. In principle, part-time jobs and volunteer work can be equally valuable to internships, for instance if they are undertaken at big-name companies or equip you with skills that are useful for consulting.
Is it worth to pay for speaking to people working in the industry? I do need some instructions on my CV/cover letter, interview and case study skills.
It sounds like you’re looking for coaching – from my personal experience as a former candidate and now as a coach, I would say it’s absolutely worth it. Working with a coach can fast-track your progress immensely, particularly when you’re at the beginning stage and aren’t really sure where to start. I’ve worked with a lot of candidates who just started recruiting and helped guide them through the process – feel free to reach out if you’d be interested in a session.