In writing up results for a Wilcoxon Signed-Rank test, do you have to state if there were no ties in the data?
Also, should the Z statistic be reported if the sample size is < 20 ?
Answering a question like "have to" would imply we knew where the compulsion would arise from... which depends on what its for. You haven't given any information by which we could judge what someone else might say about what is required. For example, if you're publishing in an APA journal there's a set of standards you can look at. Some universities or university departments may have standards for theses. Outside the standards of professional groups and journal policies et c., there's rarely a fixed standard.
Outside such standards, if you don't know what your readers will look for, you should seek to convey any relevant context which may be important in understanding your results, albeit concisely. If you include a couple of pieces of information they don't care about, it may waste a second of your readers' time. The bigger risk is leaving out something important.
I think it's important to make it clear what kind of variable it is, which generally will convey something about the risk of ties, e.g. "The response variable consists of reaction times recorded to the nearest millisecond" would indicate a very low risk of ties, while "number of spelling errors per page of text" - being non-negative integers and generally small values would be very likely to have ties. I'd also certainly state whenever there were ties and convey something about the extent. It couldn't hurt to say there are none (on the other hand you have $n<20$ you could give the entire data set in little more space, but perhaps your audience objects to seeing numbers).
With the second question (which includes the word "should"), he have the same problem -- whose standards apply? -- arises. Again, it couldn't hurt to include it as long as it's clear what the sample size is.