My pleasure to help. Let's start here:
You are stepping into a very impersonal process here, a very well-oiled machine that works on its own. No matter how reasonable you think your request or story is, no one cares. It is not because they are mean or cold. It is because they have a system and you have to follow it. There is no one to "ask" or "consider" any special request you make. Your application arrives on a certain date (along with countless others, most of whom are in the same boat as you are, ie, they too have to find a place to live, and, from that date and no other, yours is processed and stamped with an end date for your visa. Your visa allows you to enter country, which you must do by the end date. It does not mean you have to leave before that. Your visa is your initial paperwork, linked to your student status. As long you enter by that date and then present yourself to the local Gemeinde within 14 days of your arrival, there is no problem. Your visa is your entry card, not your residence card.
You are right about the straightforwardness of the documentation. If you follow it and present everything they ask for (including "declaration of departure", etc, it will go just fine).
Absolutely none whatsoever - and we have 3 cats. I have offered information on how to secure an apartment elsewhere:
Advice on new flat needed
This system works like a charm.
As for your second concern, you will find the Swiss are extraordinarily pet friendly. We have friends who travel everywhere with their cats, staying in hotels and AirBnBs. Just ask wherever you staying. My suggestion would be to consider AirBnb as your temporary location. You will be able to let them know your personal situation. Otherwise, look up pet-friendly hotels in Zurich. Again though, pardon any perceived presumption of your situation and subsequent offering of unsolicited advice on my part: if your cat does not already have a EU travel card, make sure you follow the USDA/Swiss pet-entry guidelines. If you arrive with your cat without the right documentation, you have 24 hours to send your cat back to the US or they will euthanize. This was positively reinforced and reiterated in every communication I had with the Swiss authorities before my arrival with my cats. I do not know anyone personally to whom this has happened, but still the very thought is horrifying (to me) ...
Yes we did and we almost got screwed in the process by one of the many international shipping scams in operation in the US. You might be shocked at who was the best: the US Post, International Priority. We shipped very similar items, along with our art and personal household items. If you can weight your boxes and then fill out your customs declaration online, you will save money - although price-wise, it was outrageously affordable! Fair warning: every time a box arrives, you will likely have to pay customs charges in cash to the delivery person (CHF obviously) unless you label it HOUSEHOLD ITEMS FOR MOVE TO SWITZERLAND. If they don't see that, you will pay up front, but scan the document and email the Post and you will get that money back.
I had no issues at all and you should not either, as long as you have the actual permit. Don't try to apply before then. I opened my account at UBS with an initial L-permit and my colleague did the same at Swiss Post. One my husband arrived a year later and received his permit (which by then was a B for us), same thing - without issue. Just make sure you go in with all of the same docs you used to apply for your visa, your passport, the registration documentation you will receive from the Gemeinde after you register, and your rental agreement, and you should not have issues. I too have heard the stories, but know not one person with a residence permit who had issue getting a bank account - and I have over 100 international colleagues with no such stories. This does not mean it hasn't happened, but typically there is an "underlying story" being left out of those accounts.
Again, I hope this helps.
All the best,
Jesamine