Please only submit one bug report / feature request per discussion. The "pomodoro pause" feature request has been already posted here.
I am not able to repdoduce a problem with the export date range selection. If this checkbox is enabled, you are restricted to the date range for which there is data to export:

You can also untoggle it and you can then pick any date range, but it won't export any more data.
From your screenshot it looks like you want to adjust the "start date". Your "end date" is set to June 4th - if you want to pick a later start date, you have to first set a later end date. You cannot pick an start date that is later than the end date. The Android app works exactly the same