The first two words are in a class of words called "vulgarity" or "profanity". More commonly, they are curse words. Currently, their usage is more accepted than it may have been in the past but it is still not considered polite speech. Depending on the country in which you reside, there are rules for television, radio and movies concerning these words. If the rules are not followed, fines may be levied. Suck is an interesting one. In context, it may (and I stress MAY) also be considered vulgar but, unlike the first two words, it is not vulgar on its surface. In the United States, "that sucks" at one time was considered rude but I believe today most people accept it as common everyday language and even media has no rules against the term. Slang and common language are difficult to use correctly if you have not been raised using them. Also, I as an American would be loathe to use, for example, British slang and vulgarity. Not because I think there is something wrong with it, rather because I am not sure I would know the appropriate usage in the appropriate location or setting and the appropriate people with whom to use it. YUCK!! IT SUCKS!!

The short answer is, as a learner, avoid using such words. It's not simply a case of "bad language", but also if you use them incorrectly, you will sound doubly stupid. This is a matter of knowing when and where to use them, so thinking in terms of grammar, definition or even "common use" won't help you at all. Get your level of the standard language in order first. I'm a little surprised you used those words so freely without knowing they had a negative meaning!

Let's just say that it's not a good idea to say shit, bullshit, or sucks when speaking to your Grandmother. They are vulgar. But in some situations they are used. If, for example, while you are walking you step on a stone and hurt your foot it is common to say "Shit!" Or if you are speaking to someone and he tells you a lie, you could say "Bullshit!" And sucks... for example you are going to a dance and you learn that it is cancelled and your plans are ruined... you might say, "This sucks!" Some people use these words and others think they are "bad" but it is up to you if you will use them - just be aware of who you are speaking to. :)

Yes these words do have negative connotations. I try not to use them in my normal speech. There are other better words to describe what we want to say.

These are words you should not use in a formal setting, except for suck. If you don't use "this sucks" to mean "this is bad", then it is fine in normal conversation. Shit and bullshit are generally bad.