b) You can dismiss the search bar by clicking on the search button again. However, I have now implemented your suggestion for the next release.
c) I prefer the behaviour as it is. The query passed to the API is as follows: Example search: 'nokia n900' 'nokia n900' or 'nokia' or 'n900' I'm not sure if the API discards common words such as 'of' or 'and' etc.
Setting the search order to 'relevance' should give you the same (or very similar) results to those obtained using the website. Ordering results any other way is bound to be result in false positives because idiots use tag spamming to get extra hits. Same problem everywhere on the web these days ... :/