1) It's almost always a bad idea to decide a test based on one-week's worth of data, regardless of what statistical approach you take
2) There's not really any info on why Fisher's exact test is used. It seems like most A/B software has adopted Bayesian but the ones who haven't, I believe, choose the Student's test and require prior sample sizing
3) The conversion delay issue was not addressed in the measurement plan. There are clear ways to address this issue, both tactically as well as mathematically. From a tactical standpoint, most testing platforms, you'd be able to change the test allocation to 0%, which would allowed previously bucketed users to continue to be measured with subsequent visits while not allowing any new users in. You could also just run the test long enough to where the conversion lag no longer has a major impact on results (this may or may not be possible, depending on how long and fat the lag tail is).