One. Any sample for which every population member has a known, non-zero (but not necessarily equal) probability of being selected. So long as you know the probability, you can use post-stratification weighting to help your inference to population.
Two. Both. Arguably, descriptive analysis is a special case of inferential analysis anyway.
An interesting additional distinction is between inference about a finite population (your 600 units) and a more metaphysical infinite size "data generating process" of which even the 600 units in the population are just a sample. In either case, you will be able to analyse it with the sample generated in response to question 1, but the techniques will differ slightly, particularly with regard to what is called the "finite population correction".
Three. No. But any inference you do should certainly do power analysis at some stage. It could be useful to do power analysis before determining the sample size, but this is difficult if you don't know the probability distribution of the variables of interest. Often, sample sizes in my experience are chosen with the aim of a 95% confidence interval for a particular parameter estimated from the resulting sample being within a particular range set by the key stakeholders. This is a form of power analysis and is very helpful to do before setting the sample size. But not essential if you are prepared to just live with what you get.