in some ways it's good that you're slow at the end of a sprint, that means your estimating well and not over committing, as far as keeping busy, on scrum teams I have worked on we always added research tasks for what's coming up next sprint.
This could be doing proof of concepts for things that are coming up, or looking at where to re-factor existing code, working on getting better test coverage on your code, etc.
It looks like you took some fancy items from agile development, put them to waterfall process and now you call it agile.
The product is developed for a customer who will re-sell it while
paying us royalty.
This is OK.
The team does not get to talk directly to the end user. Only to
the reseller.
This is OK. Product owner talk to reseller and collects requirements.
A product requirements document was created before starting
development.
This is not OK. I haven't seen the project where definite requirement set can be defined upfront. Change your product requirements document to product vision (short) with some initial set of requirements which are subject to change.
The requirements are rigid and do not change.
This is not OK and you will see in the future that it is also not true.
A delivery schedule was agreed on with milestones such as "alpha",
"beta" etc. and features/times attached to those milestones.
This is not OK. The real schedule will be visible from the team progress. You can make general milestones but assigning exact set of features which will be implemented in these milestones is not agile. This can change during development.
All developers on the Scrum team report to the product owner, a
software manager.
This is not OK. I would not say that developers report to product owner. Scrum process keeps visibility of the process but developers do not report anything except regular meetings. It is responsibility of product owner to be in contact with a team and as active participant see the progress himself.
Testers on the team report to a QA manager.
This is not OK. Testers should be part of development team because user story is not done until it is tested (there should be automated test to validate acceptance criteria). There can be separate QA but it is additional level of complex testing and it is usually done on customer side (but doesn't have to be) to validate that SW does what customer expects and the feedback is collected as new backlog items or bugs to existing completed backlog items.
Separating complete QA outside of development team leads to breaking the whole purpose of definition of done. Some QA must be part of the team and that part is not related to any QA manager - that part is doing commitment with development team.
The product owner has directed the team towards certain high risk
technical tasks. The output of those tasks is not usable by the end
user but rather some technology/code that will eventually be used in
the product.
This happens in every project but it should be part of some product backlog item targeting end user. It can be included directly in backlog item implemented in current iteration or it can be included as a spike (proof-of-concept) to clarify complexity of some backlog item which should be implemented in the future.
The product owner has created a backlog based on the requirements.
This is a must.
The product owner is unable to answer some questions regarding the
product. He refers to others or to the documented requirements.
This is not OK. It is job of the product owner to know answers. He has a responsibility and he must do decisions. If he doesn't know answer he must find it asap.
The team goes through the motions of Scrum. Daily Scrum, Sprint
Planning, Retrospective etc. There is a ScrumMaster.
This is OK but it doesn't mean that team is doing Scrum.
Every sprint the product owner and management decide what backlog
items the team works on.
This is definitely not OK. The product owner and management can make priorities but commitment (selection of most prioritized items) is teams responsibility.
There is a burndown chart. Scrum board with stories and tasks. The
estimates on those come from the team.
This is OK.
The team sits in an open floor "bull pen" shared with other teams,
all visible and audible. There is cross-team noise and there is foot
traffic around the team area.
It is Scrum master's responsibility to make end of this if team feels like it reduces their productivity.
The team may be required to attend various meetings not directly
related to the goals of the sprint.
It is OK, the time wasted on these meetings will result in smaller commitment (team will do less real work). It is up to Scrum master / management to reduce these meetings to increase team's velocity.
There are pressures to select certain technical solutions. Some
tools and processes are mandated.
This is partially OK. There can be non-functional requirements for tools and architecture and there can be defined processes but still final implementation is up to the team.
Best Answer
If you get more of those tasks, maybe KANBAN would be a better alternative, but you seem set for SCRUM, so lets see what you can do inside SCRUM:
SCRUM has a so-called impediment list. That's a list of all things that's keeping people from being productive. Such a task has not been planed in the sprint and doing it instead of working on the sprint goal is an impediment.
On the other hand, it seems that this indeed is a planned task. You could have a backlog item that says "handle requests from analytics" that you plan into every sprint.