This is a tricky one, and it is difficult to give specific advice. As a new councillor, you are viewing the council with fresh eyes, and it is right for you to ask questions. In fact, a lot of the information you want would ideally be publicly available through a web site.
On the other hand, small town and parish councils have a difficult balancing act. The cost of a clerk is substantial; if it is purely an administrative overhead, it can seem disproportionate to the activities of the council, and risks making the services provided poor value for money. I believe councils have to strive to keep administrative costs within bounds, as a good town or parish council can make a valuable contribution to local life.
It is likewise difficult being a clerk, as the responsibilities are wide ranging and routine matters such as agendas and minutes can take up quite a lot of time. It is possible that having a lot of work added through a new councillor asking questions could be hard to handle.
There are some ways you may be able to proceed. If there are concerns over councillor interests, they could be raised directly with the Monitoring Officer, usually the senior legal officer of the district council. You could put forward agenda items for discussion in council - if they are clear and straightforward it will not take the clerk long to incorporate them into the agenda and then the whole council can share the load of clarifying matters. You could ask the chairman for details of the legal advice, including relevant statutes. It may be possible to arrange a discussion with the clerk or the chairman to explain your concerns and to seek ways to progress them without putting undue strain on the clerk.
I hope that may give you some ideas, but feel free to ask further questions.