The most important question, Do these weekly meetings help the team? , I know some teams that do demos to the product owners after finishing every story to get earlier feedbacks and to assure thier understanding for the stories acceptance criteria
Does retrospective and showcase MUST be after the end of each interaction?
We are doing a cycle of 2 weeks for each client request leader and a weekly retrospective and show case meetings as agreed with the team.
Can we do that or is there some rule that indicates those meetings only after the end of interaction related with client request leader change?
While end of the iteration is a good time to do a retrospective and demo/showcase, if your user stories are ready and the product owner is available, it may be useful to do early demos and get the required feedback. Also for retrospectives, if there is a need to deep dive into a specific issue, it would be good idea to do a retrospective with the relevant thinking tools. It's more easier to do it at a structured frequency so you don't skip it and allows sufficient time to handle the actions decided.