The Isolated trade on Binance allows me to borrow 10x the amount I have transferred into my Margin account. My question is, does the Liquidation Price (shown in the Positions tab) trigger when I have lost all of the money in my Margin account, or, can it access the money in my Spot account as well?
If you are trading with Isolated margin, it will be isolated from rest of your fund, in spot or in cross collateral account.
So my question is really... When making a short trade through Binance Margin, am I putting my Spot account at risk or just the money in my Margin account?
You will only lose your fund in your Margin account.
You will lose all your fund (in your margin account) if you have opened Cross Margin positions. Anyway you can not say Isolated Margin is safer than Cross Margin and vice versa. It all depends upon your risk and margin fund management.