To answer your initial statement: no, I don't think they do more harm than good. The testing effect has been shown overall to improve scores compared to traditional studying (though only for long term memory, see (Roediger & Karpicke, 2006) for an interesting discussion), implying that it is doing more good than harm. This study assumes an overall positive effect without feedback to learners on whether they were right or wrong, and where students who incorrectly retrieved do not "learn" or maintain memory (Kornell, Bjork, & Garcia, 2011). Providing feedback to learners on correct and incorrect responses, however, will increase retention even for students who did not correctly retrieve, and may be one of the best ways for these students to learn (Kornell, Hays, & Bjork, 2009).
Part 1: So far as negative learning from selecting an answer, this directly relates to your third question (as mentioned above). Students who got answers correct (successful retrieval) are hypothesized to better maintain memory, while students who didn't will not better maintain (Kornell et al., 2011). Though this seems obvious, remember that retrieval rates naturally decrease over time (the goal is to maintain a high retrieval rate).
Part 2: In a word, yes. Given this, they each measure different things (and should be used for different purposes). Personally, I use a "post-lecture" quiz as an "exit-ticket" (sorry, background with high school freshman) to quickly check where misconceptions lie. These quizzes are reviewed prior to students leaving the class in order to identify and address misconceptions (formative assessment). I've found that waiting can allow more connections to be made (and thus, higher level responses), but if the material is not encoded correctly false connections can be made (reinforcing incorrect information).
Part 3: Not reviewing the quiz is hypothesized to create a "bifurcation" where those who got answers right better remember, and those who did not get the answers right steadily decrease (again, a natural pattern in retrieval over time). The "testing effect" exists because overall students are theorized to do better, but again, there will be a split in student growth between those who remembered and those who didn't (Kornell et al., 2011). Reviewing the quiz immediately (if paper, go over the answers right after the quiz!) is hypothesized to help all students, regardless of whether they initially got the correct answer or not, and thus would be the recommended method to improve students' knowledge retention (Kornell et al., 2009).
To summarize: review after taking quizzes acts much like a "studying" effect (where those who got right and wrong answers can learn), while quizzes without review are hypothesized to split learning (those who correctly recall retain, and those who fail to correctly recall don't retain). Both groups are able to be helped through quizzing and reviewing answers.
Kornell, N., Bjork, R. A., & Garcia, M. A. (2011). Why tests appear to prevent forgetting: A distribution-based bifurcation model. Journal of Memory and Language, 65(2), 85–97. doi:10.1016/j.jml.2011.04.002
Kornell, N., Hays, M. J., & Bjork, R. A. (2009). Unsuccessful retrieval attempts enhance subsequent learning. Journal of Experimental Psychology. Learning, Memory, and Cognition, 35(4), 989–998. doi:10.1037/a0015729
Roediger, H. L., & Karpicke, J. D. (2006). Test-enhanced learning: Taking memory tests improves long-term retention. Psychological Science, 17(3), 249–255. doi:10.1111/j.1467-9280.2006.01693.x