zaptor: 
Tethering is not allowed with the $30 plan. I would've gone with with this for the other phones if not for the fact that you only get 100 mins talk time.
Any phone activity for a new day (voice, text, or data) will trigger the $3 charge. If you have the phone off for the entire day's billing period, then you won't get charged.
You'll get charged if you're roaming. If you have a US number (in the US), you won't get billed if you receive a non-local call. However, it may cost the caller a non-insignificant fee to call you on your US number.
We have number that we roam on (has to be postpaid). I deliberately choose a number for a regular SIM, because I could simply install it into the lightweight non-smart R100 phone we use as a hotline if anyone in NZ needed to contact us. In that instance it costs $1 USD per minute (rounded to nearest minute) for us to receive a call. Because of the free minutes back to NZ, I hang up and call the caller back once they've contacted me. Good postpaid plan (if you wanted cheap roaming), is Vodafone's $10 mobile plan for ex-TC customers, assuming it's even still available.

I'm thankful I opted for the unlimited voice plans - whenever we split up we end up calling each other, and I've also had to make a number of non-family calls for other things (taxis, hotel, stores), in addition to touching base back at home for other things.
Btw, $3/day plan can't have add-ons applied (i.e. international calling, $15 day big data add-on).