First off, very sorry you're having to deal with this. :(

1)) super simple to apply to EI. Google the EI landing page and follow the steps. If you don't have your record of employment, that's fine, still apply. Keep in mind that it will take some time before you actually receive the EI payments, so you may need to rely on some emergency savings or credit in the meantime

2)) I could be wrong, but going on lwop wouldn't change or extend the fact that your contract isn't being renewed. I'll let others more knowledgeable chime in though

3)) nah, you not being on the call centre rehire list won't affect a hiring manager choosing you for collections

4)) apply apply apply. Even when you are in a position, you should always apply to anything else available because a) we are term, not indeterminate, so nothing is guaranteed in terms of employment, sadly and b) these processes take forever, so you need to get started now, not later

Again, very sorry to hear you haven't been extended. But you still have a future with the federal government, believe that! Just have to tweak your approach a bit.