SMS - STOP and HELP?

Hi,
I set up a SUBSCRIBE shortcode and texted “SUBSCRIBE” to the right number.
It subscribed me by replying with my message and marking my contact as ‘SMS Opt In’.

Then I replied with STOP. It replied with the carrier’s default unsubscribe messaging.
It didn’t change my contact from being “SMS Opt In”. In other words, maybe the carrier knows I opted out, but Vin65 doesn’t.

I then tried SUBSCRIBE again, and it didn’t give me any response at all.

Question 1: Did it not re-subscribe me because only Vin65 knows about the inbound message “SUBSCRIBE”? And I didn’t get a response because the carrier thinks I’m unsubscribed still?

Question 2: How do I resubscribe with the carrier?

Question 3: Is there any way to have “STOP” change my vin65 contact status?

Question 4: Why didn’t I get an email “Received Text Message” with what the textor wrote except when I sent “STOP”? It didn’t email me with the first “SUBSCRIBE”, nor subsequent “SUBSCRIBE”. Do i have to turn on email receipt for inbound messages when I create my own somehow?

One more question: Line 1 of the default/canned SHORT CODE TERMS OF SERVICE page says this: When you opt-in to the service, we will send you an SMS message to confirm your signup.

Is this true of all 3 means of opting in?
https://documentation.vin65.com/Text-Messages/Text-Message-Opt-In-Out
(Website, shortcode, and Admin opt ins)