If you wind up not using it Saturday, I would definitely bring it back to the boil (not too hard) for at least 15 seconds before cooling it and puting it back in the fridge- sanitation procedure for keeping a stock low in harmful bacteria.
You really should do it every 2-3 days- stock is way too inviting a medium for bacteria production- if you don't use it, freeze it!
Yes you will be fine. The only thing I would mention is when you make the stock, cool it down as quickly as possible. After straining I transfer to a big bowl and set in sink in a bath of icy water. You can also put some frozen plastic water bottles in the bowl. The longer it sits at that warm temp in the cooling process the more likely you are to start off on day one with a risk prone stock.