Shouldn't be $.30 per minute. From what I've gleaned of the information page (https://support.t-mobile.com/docs/DOC-4826#fifthheading) it eats $3 of whatever is in your prepaid account per month, gives you a combined 30 minutes (which would be $.10 per minute) or 30 texts ($.10 per text) with an additional $.10 incurred for any minutes or texts above the limit. It's technically a better deal than the old legacy plan as far as cost per minute/text, but as I inquired about in my new thread from a few minutes ago, the information page is ambiguous as to whether unused minutes roll over each month. I use my phone so little that even at a slightly higher cost per minute, it's just more convenient for me to buy a $10 card once a year as I've still got close to $100 in unused balance accumulated.
"randomly", or is it 30 days later?
Well, it's not 30 days later from the previous 17th, but if you didn't pay attention last month that it might have moved to the 16th, you'd be still thinking that.
Prepaid plans are for 30 days for a month, not a calendar month.
By default, you get switched back down to the $3/mo plan, for whatever reason. That's why it came there.