Let me cover your questions one by one:
There are some headers on css, that related to broswer support - what shall I put on css.
You should definitely be using a CSS "reset". There are a number of these available, but the basic idea is to get rid of the differences between the default behaviours of various browsers. See this question for more on which one to use.
Should I avoid using, i.e 1px, and instead use : 1em (or relevant ratio) on my css file.
px
and em
both have their place. They're both good to use. em
is better in some cases for making your site scalable, but there are plenty of good reasons to use px
, and it's also perfectly valid to use them both in the same site. My advice: use whatever works best for you in any given situation.
How far can I go for support (i.e IE 5 is old enough, that doesn't worth the time I may spend to support that browser? (I need to know how much it is used arround the world).
You're right, IE5 is long forgotten. Most people I know have also now dropped support for IE6 and IE7. Both of them are down to virtually zero usage in most countries. If you have a specific need to support them, you will know about it already; if not, drop them. They are both missing some important features, and dropping them will make your life a lot easier as a developer.
For Safari, you'll need to support a few versions, as people with Macs often don't upgrade their OS and may be stuck on a lower Safari version.
For Chrome and Opera, you only need to support the current version.
For Firefox, you need to support back to FF17 (the current extended support version).
You should also consider mobiles. You need to make your own decisions about this; there's a lot of mobile devices out there, and a wide range of browsers and versions.
I need some guidelines for best practice, and that my site can be runnable at most browsers.
Use sites like http://CanIUse.com to check browser compatibility for any specific features you want to use. If you need to use a feature that isn't supported in some browsers, you may still be able to use it by making use of a polyfill script. But don't use too many.