Leaving Bahrain with active CC + phone lines

As long as the amount is being paid, there is no issue. 

And they only stop you from leaving if you have stopped paying for a while and the service provider has filed a case against you on which an execution court has issued travel ban.  This takes time and is not linked to the visa.

The bank account and credit card will remain valid until the expiry date of your passport, residence visa and / or CPR in the bank records.  Once that date is reached, the bank will notify you for a few months before shutting off the accounts.   There is no direct link.  However, if your employer transfers end of service to Bahrain bank account, the bank will know in advance and can disable accounts / cards.  But again, it has nothing to do with immigration.   Immigration is only involved if there is a case as above.

Lastly if my visa is cancelled will be the bank and service provider will be notify and alerted?

Read what I wrote - there is no direct link.

If the account + cc is on freeze, what we can do to unfreeze it or to make it active again? thank you

Depends on what it was frozen for.  If it was due to end of service coming into the account; no way except to either pay off the loan / credit card or show them a valid visa / contract with new employer.

New visa and/or contract from new employer here in Bahrain only? What if I got a job outside bahrain. I accepted job in Dubai with ready employment visa and contract with higher source of income. Can I present these to the bank?