Regarding clothes and car seats, each county, in each state has its own rules.
In my county. we have to provide our own. They generally do not lend them out. We get a pretty good clothing allotment twice a year, not sure how it is in other places.
I agree, you should document whatever clothing they came with and talk to the worker about what is needed.
If you haven't already, try
www.freecycle.org to see if there is a freecycle group in your area.
That is how I got the toddler seat that I am going to need when our foster baby outgrows his infant seat in the next few weeks. It was also helpful in providing baby clothes for a little girl who came with nothing.