1. I suppose this depends largely on how noticeable the change will be after binding. If you are already wearing baggy clothing and such that make the chest appear smaller, the change may not be too great. Alternatively, if it is on the larger side and/or you have previously not make any conscious attempts to hide or de-emphasize it, then it could be quite noticeable. Immediately taking the binding off and storing it in a safe place upon coming home could be one way - we really shouldn't be wearing it 'full-time' anyway, even though most of us still do.
2. I've heard a lot about ace bandages - this combined with the layering of undershirts seems to be quite effective especially for bigger sizes. I am very fortunate to have a manufactured binder, so I've not much experience with any other method - but there are many testimonials out there on the internet. YouTube is a great place to search.
3. In the short-term, bind sensibly; in the long term (I would say for 5+ years continuously, some would argue for shorter or longer), realize that binding is not a permanent solution. Taking the binding off whenever it is not absolutely necessary is an important part - especially when we are young and our bones are still growing. After growing accustomed to binding, it can start to feel like it is a necessity 24 hours a day, but I'd say to use one's own sensible judgment there.
I would definitely recommend trying to get your hands on a decent binder as soon as possible - risk of acute (and long-term) injury due to incorrect binding methods are much higher when binding without one. If you live in the city, are there any local trans groups around? Someone I met from a group helped me order mine with their credit card and had it sent to their home. Online communities are another place to look - many pass along their binders for free after getting top surgery. If you do find a match (this can take a while... be patient), could you borrow a trusted friend's address and have it sent there, perhaps?
Here is one of the guides that I would personally recommend, if you've not seen it already.
Hopefully that helps. Feel free to PM me for anything any time.
"If limitations exist, it is because we have erased the possibility of potential."