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I have named plugins/system/admintools/admintools/main.php to main-disable.php, then i got in one time, but after trying edit the article, or add an image, and when i clicked "save" it threw me out again.

If you did that and the problem persists then it's not coming from Admin Tools. When you rename the plugins/system/admintools/admintools/main.php file your site can no longer load Admin Tools' code. Therefore the problem you are experiencing is with the host.

Actually, loading the page for ever and ever, it didn't even give the warning "you are spammer, hacker or otherwise bad person".

Yet another conclusive indicator that it's a hosting issue.

This morning i got in once again, and managed to save my ip to whitelist, and remove my own security exceptions. Then it locked totally again, and no hope even getting to live site.

You keep adding nails to the coffin of this issue. It's definitely a hosting issue.

My client can get to live site though! So i blocked out the server problem...!

This is a false conclusion since your client is not using the same ISP, IP address, browser and computer as you. Considering that the host may actually be blocking you because of what their server mistakes as an attack patterns your conclusion seems to not be grounded on any facts.

I even managed to login via ipad, with another wifi, but when i save something, or anything, it goes again to white page, loading forever...

This, again, points to a server issue. Have you not spotted the pattern yet? When you try to save anything it locks you out. This points me to two possible directions:
- A server module such as mod_security2 or mod_evasive which mistakes your requests as an attack.
- A networking issue, plausible only if you and your client are on different countries.

In case you don't believe me you can simply completely delete plugins/system/admintools. This means that Admin Tools' code can not load (since it's no longer there!) and replace the .htaccess file with the stock one from Joomla!. If your problem persists you'll know that it's something coming from the server. If that magically fixed everything your issue was something in the .htaccess file.

Again, when you rename the main.php file or delete the entire plugin folder there is no Admin Tools code being loaded. In the first case it can't load because you renamed the file. In the second case it can't load because it's not there. Based on what you are saying you did neither, making my explanation invalid since it was based on the assumption that what you said about renaming main.php was true.

As for IPWL it's something entirely different. It's the administrator IP whitelist (you tried to access the site from an IP address which is not in the whitelist). However, this is either an old log entry OR you have not renamed the main.php file. In the former case it's useless and irrelevant. In the latter case try actually renaming the file, log in and then disable the administrator IP whitelist from the Configure WAF page.