P. 183 of the Handbook of the IPA (1999) lists the character and identifies it as a syllable break. The latter example illustrates the well-known fact that syllable breaks are higher level phonological abstractions rather than direct phonetic observations. Many people maintain that the syllable break in "courage" is before the rhotic, and many people maintain the contrary position that the break comes after it. The former transcription with ".nt" is, uh, rather anomalous but maybe someone has a syllabification with [nt] in the onset. I can't say I've ever seen that, though.
The slashes and brackets are not phonetic elements, they are notations signifying kind of analysis. They too are identified, p. 175, as enclosing phonetic ("") versus phonemic ("//") transcription. IPA does not posit a theory of the difference between phonetic versus phonemic. Actual usage is highly variable, where slashes might mean "underlying" or "some derived pre-phonetic representation", and brackets mean "any non-underlying representation". To understand an author's use of brackets and slashes, you have to understand their theory of representational levels (and the rules of the journal that they are publishing in).