Hey Josh!
I'm not sure where in the book you are referring to, but the equation does contain a negative sign. There's an example on CC pg 300 with the negative sign. Let me know what page this was on, perhaps it was an typo.
Its always negative. The only time it will be changed to be positive, would be due to one of the terms that is also negative (either T or S).
ΔG=ΔG0+RTlnQ can be used when you are looking to determine the Gibbs energy during a reaction, when the reaction is not at equilibrium, to determine the spontaneity of it.
Yes! So entropy is a factor in determining spontaneity. There are a few cases of what would yield a spontaneous reaction, and its implications for high/low temperature. On CC pg. 300 bottom of the page, we have a summary of the trends.
Overall, you need -TdeltaS > deltaH to have an overall negative deltaG.
And don't be sorry! Happy to help :)
Hope this helped, happy studying!