I'm going to have to argue with 1a
I start every almost every phone call to anywhere with the questions like that, eg. "Can I renew my insurance?", "Can I order a takeaway?", "Can I book a ticket". I do not know how else one could possibly start a phone call of that kind.
(Cuthbert Annihilator, Mon 7 Sep 2009, 20:50, 4 replies)

You could ask
MAY I renew my insurance.

Of course you CAN do it, that's what the company is for, if you're trying to be polite ask if you may.
(misskitty reeks of sex and turpentine; laudanum afternoons, Tue 8 Sep 2009, 4:35, closed)

Ah, correct English....
Practically unheard of in these God-forsaken times.
( Monty Boyce, My cheese game is strong, Tue 8 Sep 2009, 13:26, closed)

You're sort of right, there
I always do the "do you want my account number" bit, but it's really a shorthand for "do you want my account number NOW or do you have to access something on your computer first, and therefore not stop me halfway through because you're not ready."
(greatoldone Ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl f'tagn, Tue 8 Sep 2009, 7:15, closed)

I do this and think every time - why am I saying this?
As I call for a taxi and find myself saying "Can I get a taxi please?" my mind cringes as I imagine the operator wishing a quick and instant death on me...
( snee held his breath since, Tue 8 Sep 2009, 10:38, closed)

I start with
"I'd like to..." (order a takeaway, book a cab, query a bill) and then wait for the first question that's in their flowchart.

I also lack the ability to predict (and the inclination to keep notes on) whether each particular company prefers to start with my account number, or my name, or my postcode, or my query. The call taker has the flowchart in front of them and knows what information they need and in what order. I don't.
( Batsgirl, Tue 8 Sep 2009, 12:11, closed)

I do this too
it's simple and easy- you tell them what you want and give them control of the conversation so they can ask you what they need to know. Then you can both hang up and go your seperate ways.
(Evilweevil is covered in bees, Tue 8 Sep 2009, 12:18, closed)