Yes, you should still be designing for 1024 monitors. A width of 960px is a generally accepted guideline.
You should definitely be using ems for font size, though I know they can be a little tricky to wrap your head around. Chris wrote an article not too long ago that sort of goes over all of the different ways to size fonts: http://css-tricks.com/css-font-size/
Yes, the margins changes and all the scroll comes.
Should I be designing with 1024×768 to avoid these scrollig?
Somebody suggested me that I should use "em" instead of "px". I think that they are used only for font sizes, and not for setting up various sections on the page.
Also, should I be using "%" instead of "px".
As I am new to web designing, I wanted to ask this here, so that I can get proper suggestions.
In my experience many will preach about fluid layout and how the dynamics of a fluid page is that much more compatible and unassuming and graceful and blah blah blah..
pretty much most professional designs you will see won’t be fluid. Simply because by setting a solid acceptable width (960px being the norm, as thedoc said) you have far greater control of content layout, design elements so on and so forth. While the concept of usability and cross computer compatibility seems to scream fluid sites are awesome; they will almost certainly compromise the design of your site. (or at the very least give you a massive headache during the markup of)
And ultimately the control and precision you gain from using a static width in my opinion offsets the supposed extra usability of trying to conform to the fluid model.
I personally wont be embracing fluid sites without a really good reason