Twilio expert

I am wanting to forward a call from my Twilio number and maintain my Twilio "Friendly Name" in order to know which "business line" the caller is utilizing. Need to have the caller ID show up as "Friendly Name"
Then have a SMS message sent to show the Caller's Name and Carrier Information to the same number that the Twilio call is forwarded to so we can have a log of incoming calls in call log and SMS log.

I wish to do the following:

Call request:
1) A caller dials my Twilio phone number.
My provider calls my Twilio phone number
Twilio looks up the number using the Lookup API
Twilio shows caller ID as the "Friendly Name" associated with my number
Additionally Twilio sends me an SMS with the Caller Name* and Carrier information
Twilio forwards the call to my phone number with my "Friendly Name" as caller ID so we can appropriately answer the call with correct business name.
We will need this done with My TwiML Bins or Studio Workflow if possible. We will set up about 5 total numbers

SMS request:
2) A user sends an SMS message to my Twilio number
The Twilio SMS is forwarded to a US cell # to notify me of a new message
I want to be able to reply directly from my mobile device where the SMS has been forwarded. Without logging into Twilio or a 3rd party app

Can the system be set to receive and respond to SMS from a forwarded number?