The second and third sentences are examples of what I call the impersonal imperative. It's a feature of German that does not exist in English, but it's still a form of the imperative mood; there's no rule saying that a language has to have just one. It's used when no one in particular is being addressed, so instructions, recipes, signs, etc. It's also frequently used in question form for computer prompts. Grammatically, it's just the infinitive of the verb placed at the end of the sentence where infinitives naturally go.
The first sentence is a bit of an anomaly. My thinking is that it's probably an ellipsis, or a fixed phrase. It is a common phrase though and translates as "Enter at your own risk". One could argue that neither the German or the English is an imperative, more of a warning, though grammatically the English is an imperative in form. (Literally construed, the English version does tell you to enter and assume the risk, even if that wasn't your plan.) In any case, the German version is not technically grammatical according to the usual rules. Either there was a Sie that was dropped, or the verb was moved to the front for emphasis, or Betreten is meant as a noun (entry) and another verb (probably sein) was dropped. However you explain it grammatically, the meaning of the sentence is clear. In German, as in English, the important thing to communicate the message, not to exhibit examples of perfect grammar, and you sometimes have to allow for a bit grammatical rule bending in everyday speech.
PS. Bruce Duncan's grammar site has an explanation of the impersonal imperative which is accessible for learners. He uses the phrase "General directives" so search for that or look for the sign with a plate and silverware. It's also mentioned in the German for English Speakers site where they call it the "infinitive imperative".
