Hi and welcome!
Well in terms of advice, don't expect SWs to work/behave professionally. That way you may be positively surprised - some SWs are brilliant!
But even the brilliant ones struggle with big caseloads and lack of resources. So things like lost paperwork, pointless delays, doubling up of things that have already been done - par for the course.
Photocopy everything you send/give them. Keep your expectations low. Always expect things to take longer than you would expect in other contexts.
FWIW from when we sent our 'registration of interest' it took another 2.5 months to actually get 'registered'. (A while after we had sent it off, they came back to us saying that there had been some miscommunication and they wanted to repeat the initial home visit, so we waited for the SW to have time for us, then waited for the SW to write up the report, then waited for the report to be discussed in the team/seen by the team manager, then waited again for them to actually notify us of their decision.) Needless to say, we didn't make it onto the prep group that had been planned for us. Nor onto the next one.
But hey, these are annoying but very minor niggles, in the big picture
Good luck with this exciting, life-changing journey!