1) Perl does not have integer division operator. It must call "use/no integer" to change type. Python has: / - normal division, // - integer division. Sugar. To use things such as "ceil/floor", I need to "use POSIX"... Aren't they basic?

Who cares about integer division? It might be useful for academic homework (such as looking for prime numbers and the like), it is just mostly useless in real life. I can't remember of any real life problem where I used integer division or wished I had one. Same with ceil/floor, you have int, you can do what you want.

2) It is not problem for me to read dollars in single variables. But it is annoying to read them in some-dimensional arrays (it's noisy), e.g. $array$i$j > $array$i$j-1.

I can understand your point, but the language has to be consistent. Variables need sigils, so be it. I was using Python before I started Perl, and I can remember that some people criticized Python for the indentation. I disagree with these criticisms, I feel that Python found an interesting way to do things. Having said that, the good thing about sigils is that you're almost certain never to use a reserved word.

3) It is strongly recommended to "use strict" and make variables "my", then why it is not default? Whay all the code must have so much my my my my...?

History. Backward compatibility. No time now to go through the other points, but you get the idea.