If the most important thing you have to say about yourself is "I went to University somewhere you've not heard of", that's going to create a poor first impression.
You say that:
The thing is, I have the longest experience among all of them, at a known company.
So if you think your experience tells a better story of who you are and how you're qualified than your attendance at an educational establishment, why isn't your experience section first?
My website is not even visited in the time period between submission and application rejection. So they are not even checking it, even though it is near my contact details at the top of my cv.
You will put hours into your CV and read and care about every word. Employers won't. They will look for the highlights, and that means you need to communicate what you can offer as quickly and concisely as possible. You also need to avoid unforced errors which leave a bad impression.
Recruiting managers probably won't visit your website unless they've decided to interview, and even then, don't count on it. They might not spend more than a couple of minutes looking at any one CV, and they will probably skip the contacts section. They only want to contact you if the rest of your CV tells them they want to interview you.
Can a low prestige university name be a deal breaker on my resume?
It can certainly affect your chances, although what might be especially important in any technical context is if the course has a poor reputation in the subjects they care about.
If you're applying to over 20 jobs and consistently getting rejections, that suggests there is something odd about your applications. It might be your university, but it could also any of be a host of other things. Normally there's no way of knowing why you've not been shortlisted. But if it is university, well, you can't do much about it - focus more on the things you can do something about.
- Do you follow the application instructions? e.g. if they ask for a cover letter and CV, do you send both?
- Are your applications professional, presentable, accurate and understandable, including spelling, grammar, typesetting, etc.?
- Does your application demonstrate you will be able to the criteria marked 'essential' on the job advertisement?
- Does your application demonstrate you have been entrusted with a level of responsibility substantially similar to that of the job advertised?
- Do you just list your current job title and dates worked, or do you summarise your responsibilities and achievements?
- When you talk about projects, do you communicate what you did, what you used, what difficulties you overcame, or merely that you "worked on" something?
Find a couple of your contacts (preferably the ones who got good jobs) and ask them if they would mind looking over your CV to see if there are any gaps or red flags.
If you can give the impression "I already know how to do this job - I'm doing something similar already", then for most jobs - certainly development jobs - that's a far better indicator of whether you're likely to be a good fit for the job than university attendance.