1) While a developer is coding a task, it is impossible for a tester to test
it (it doesn't exist yet). What then
is the role of a tester at this point
The tester may still create test plans and have a list of what tests will be created. There may also be the need for the tester to get training if the development involves some off-the-shelf software,e.g. if you are doing a CMS project with Sitecore then the tester should know a few things about Sitecore. There can also be some collaboration of the tester, the developer and the end user or BA to know what are the requirements and expectations so that there isn't the finger pointing that can pop up in vague requirements.
2) Is the tester now involved in unit testing? Is this done parallel to
black box testing?
Not in our case. The tester is doing more integration/user acceptance testing rather than the low-level unit testing. In our case, unit tests come before any QA tests as the developers creating the functionality will create a layer of tests.
3) What does the tester do during a sprint where primarily infrastructural
changes have been made, that may only
be testable in unit testing?
Regression testing! In making infrastructural changes, did anything break? How thorough a testing suite can developers run compared to QA? We had this in a sprint not that long ago where most of the sprint work was plumbing rework so there wasn't much to test other than seeing that things that worked before still work afterward.
In our case, we have testing as one level up from our development environment but still a pre-production environment. The idea is to allow QA a sprint to validate the work done and for any critical or high severity bugs to be found and fixed before a release into staging for final user acceptance testing, so if developers are working on sprint X then QA is validating sprint X-1 and production may have sprint X-2 or earlier running depending on the final UAT and deployment schedule as not every sprint will make it into production after QA gives the OK to move into staging. There are pairing exercises that can happen once a developer is done an initial coding of a task to ensure that both a tester and an end user sign off on what was built. This is our third or fourth version of trying to integrate quality control into the project so it is still a work in progress that has evolved a few times over already.
