Should I test my website against all browsers & all versions?

Prob 1 : Do I need to care about some bugs of Firefox 2, firefox 3, chrome7,8, opera 8,9... etc that can make my site look weird on these old browser ? I wonder if the developer changed the HTML-render-engine everytime they update their browser & make my site imcompatible with all version.

Will almost visitors keep their browser up2date ? If not, please suggest me with some tools that can help me test my site against FF, Chrome, IE, Opera, Safari in all major versions. (I've try this by some online services but it's extremely slow to take screen shot of my site)

Prob 2 : Is there any difference among browser for PC, Tablet, Mobile (except the screen resolution) that can cause a display error for my website ?

Thanks a lot!

Solution

Well, whether you should test your website against:

all browsers: Yes, because Windows users have any among IE, Chrome, Firefox & in remote cases, Safari, Opera among others. Whereas Mac users will have Safari, Chrome as their preferred one.
all versions: Probably no. Limit yourself to only those which are still supported, i.e. IE 7 onwards & so on.

But, the key lies in the engine upon which the browser is based upon. It can be said:

                     *OS: Kernel :: Browser:Engine*

For instance, Chrome, Safari, both are based upon "webkit" layout engine. Check out, web-layout engines: http://en.wikipedia.org/wiki/List_of_web_browsers

(This consideration will save a lot of effort as you can be rest assured that browsers using same engine will behave in a similar manner.)

Also, keep in consideration your target audience, this can help you limit your browser choices.

And yeah, most browsers have developer tools (F12 key), which allow you to simulate the previous versions of the browser.

But, all in all, the answer is relative & depends solely upon how much time you have & how much effort, time, testing are you willing to spend...