I don't understand. Does your site have .html files that need to be parsed as .php? AND .htm? AND .shtml?

by "bad url's"
do you mean url's that do not exist?

what do you see if you enter

www.example.com/index.html/folder1/folder2/index1.html

into your address bar?

From the 1and1 help center page for "Manually Set the Version of PHP Using an .htaccess File [help.1and1.com]", the examples use AddHandler, not AddType ...?

AddHandler x-mapp-php5 .php

If I put slash after any URL from my site it displays the same web page but all links are wrong.

This has nothing to do with Apache/PHP handlers. This is because you are using relative URLs in your page, and is to do with how the browser resolves these URLs. (You might be able to set a BASE element on the page to resolve this, without having to update all your links.)

My site has html files from which I am serving Google adds using "php include" and the only way to have is by adding
AddType x-mapp-php5
in .htaccess.
AddType x-mapp-php5 is from 1and1 support and I also tried
AddHandler x-mapp-php5 .php, but nothing changes.

by "bad url's" I mean url-s that do not exist
when I enter
www.example.com/index.html/folder1/folder2/index1.html
I see
www.example.com/folder1/folder2/index1.html page but no images.

"/" after any normal url like
www.example.com/index.html/
has nothing to do with my browser - if I put slash at the end of this post url I get 404

"/" after any normal url like
www.example.com/index.html/
has nothing to do with my browser

Unless you have additional server-side processing to trap this (which is probably what WebmasterWorld does) or you are manipulating your URLs in some way (semi-pretty, MVC-like, ...) then this has everything to with the browser.

Without any additional server-side processing, a request for "example.com/index.html/hello" will normally result in the server returning "example.com/index.html" (where "index.html" is a valid page and "hello" does not exist). However, the browser thinks you are at "example.com/index.html/hello".

Any relative path in the client-side page (anchors, stylsheets, scripts, ...) is now relative to "example.com/index.html/hello", not "example.com/index.html". So, if you had a relative link to "folder/page2.html", the browser is now going to request "example.com/index.html/folder/page2.html", not "example.com/folder/page2.html". As mentioned above, "example.com/index.html/folder/page2.html" is going to "successfully" (200 OK) return "example.com/index.html" (again!), but the browser now thinks you are at "example.com/index.html/folder/page2.html", etc. etc...

when I enter
www.example.com/index.html/folder1/folder2/index1.html
I see
www.example.com/folder1/folder2/index1.html page but no images.

...so you do already have some URL redirection?

yes, I have many re-directions
but how Google gets all those abnormal compilations from my website? many thousands!

And I also tried your suggestion
example.com/index.html/hello
with my friends websites and got 404 for all such requests

And final testing point: if I remove from my .htaccess ONLY the line

AddType x-mapp-php5 .php .html .htm .shtml

all is back to normal i.e. I get 404 for all variations mentioned above including slash behind. For all! with the same browser.

The issue is with Path Info, which by default is handled differently in html than in php.

:: detour to look up, because I get it backward every time ::

"Off" = if there is more stuff after the end of the URL, the request gets a 404
"On" = extra stuff after the end of the URL shows up in browser's address bar but doesn't affect request
"Default" =

The core handler for normal files defaults to rejecting PATH_INFO requests. Handlers that serve scripts, such as cgi-script and isapi-handler, generally accept PATH_INFO by default.

See what happens if you add the line

AcceptPathInfo Off

This is a core directive. It can go anywhere, but it's best to put it near the top of your htaccess so you remember where it is.

AcceptPathInfo Off

No changes