I expect that I will be billed tomorrow, Dec. 13, for service for from Dec. 13, through Jan 13, and it will be posted to my credit card soon after. My last bill was my first bill from them and for some reason it was not posted until 12 days later. It could be that Google's accounting system on a first bill takes awhile to set up thus the delay. The other thing is that one has something like 14 days to return a phone if you don't like it and maybe they build that into the billing system. I don't know. Then again, the 12 day delay may be common for their billing system. I'll report back when I see a charge on may credit card for my next billing period.
Project Fi is a prepaid plan much like others such as Straight Talk (Walmart), Virgin or Cricket, or other MVNOs. These plans purchase minutes and data from the other carriers like AT&T, Verizon, Sprint or T Mobile and sometimes roaming access. Prepaid means exactly that: you pay in advance for your service which usually includes unlimited minutes and text with a certain amount of data per month. There is no contract and service can be dropped at any time. Straight Talk is a bit unusual in that its main plan allows one to activate a phone using one of the big four carriers' towers and get 5 GBytes of LTE if available per month for $45. Once you reach the 5 GB of data speed is reduced to dial up. One can set up payments for more than one month up to a year in advanced and save some money. You can buy phones from Walmart or bring your own unlocked phone that will work on the carrier's towers you want to use and purchase a SIM plus at least a one month's subscription. My wife uses this and it works well for her on AT&T.
Project Fi is also an MVNO but with a couple of twists. It has unlimited voice and text like other MVNOs, but uses two carriers, T Mobile and Sprint plus roaming but also can make use of WiFi for its voice and data. It's supposed to be able to automatically switch carriers if one of them has no signal. If one is using a hot spot WiFi and walk away from that signal your Fi phone should switch to one of its carriers automatically. Further more, if you use less data than you paid for in a month you get a credit on the next month's bill at $0.10 per mega byte. Most other MVNO data plans are use all your data you paid for or lose it or if you go over your allotment you pay very high fees for it. The other advantage of using the new Nexus phones purchased in the US is that they can use both GSM towers (AT&T, T Mobile) and CDMA towers (Sprint and Verizon) in the USA and some overseas. I guess there are international Nexus phones as well. If you visit 120 foreign countries with your US phone you can make inexpensive calls, use WiFi to make free calls there or to the US. Others in these threads have posted about their experiences in that regard. All these features make Fi pretty slick.
Sorry if this last discussion about MVNO plans was obvious to you, but I assumed, probably wrongly, you are a newbie to this paradigm.