TASK DEFINITION: Given a travel related situation, and given a specific question about the situation, summarize the question into a title
PROBLEM: My problem: I recently booked a business trip about three months out, noticing slightly too late that there's a huge event (Formula 1 race) happening in town the previous weekend and all the remotely convenient and/or comfortable hotels are asking crazy rates (US$500+).

The usual rule of thumb of booking flights and hotels is the earlier the better, since prices usually go up but rarely come down. In this case, though, I have a sneaky suspicion that hotels may be demanding too much and there may be a fire sale of unsold inventory right before the event.

So: Do hotel prices generally go down right before big events? Bonus points for answers with data instead of just speculation.

(Note: this question has been edited, as I'm more interested in the general question above than the specifics of my situation.)

Interim answer 1: I've followed simbabque's answer and booked a mildly inconvenient and mildly crappy but fully cancellable and not crazy expensive hotel to cover my ass, and will check & report back on the hotel situation before arrival.

Interim answer 2: Idly poking around, I noticed that a big chain hotel near the office that had previously been 100% full had a room free for all three nights at our normal corporate rate (~US$120). Booked! But I'll still check before arrival and report back for science.

Very overdue final update: I didn't do a very thorough check because work, but a casual browse on Google Hotels did show a bunch of hotels offering rooms at less stratospheric prices (under $300). YMMV.

SOLUTION: When should I book my hotel if prices are inflated due to a major event?

PROBLEM: I am trying to use Google Maps in China. I know that Google is blocked, which is why I downloaded the map of Beijing offline. However, when I open the app my phone attempts to find GPS satellites but finds none. I know location works because my location works fine when I am on WiFi. Is this a China blocking GPS thing or something else?

I am using a Verizon HTC One (M8) with Android 5.0.1 and HTC Sense.

Note: This question has also been cross-posted to Android.SE.

Update 1:

All my testing for this question was done on the 7th floor of a downtown office building. Yesterday after waiting a while, I was able to recieve GPS signal (using both Google Maps and GPS Status) while on the 17th floor of a suburban apartment building. I was then also able to recieve signal in another part of downtown that lacked many tall buildings. When I get back to the office tomorrow I will be able to judge if it was just taking a mega-long time to get the satellite data as @Vince suggested, or if it is the urban canyon as @Loren suggested. Thank you all for the help and explanations!

Update 2:

After some testing, it seems that this does simply come down to an urban canyon problem. The GPS does not find any satellites at my desk in the office, however, if I bring it next to a window it finds 2 satellites (not enough for a location, but enough to answer this question). When I take the phone outside the building I am able to get location in some areas. Thank you all again for the help and the wealth of new knowledge.

Note: all testing was done with data and WiFi services turned off.

Based on a comment, I have asked a question in GIS.SE asking about the urban canyon and how it compares to Beijing versus NYC.

SOLUTION: Why does my phone's GPS not work in China?

PROBLEM: What happens if I leave Moldova through Transinstria? I guess I won't get a Moldavan exit stamp, would that be a problem if I visit Moldova again? Wouldn't it look like I overstayed in the country illegally?

SOLUTION:
Can I leave Moldova through Transnistria?