Re; dotted resistor.
I was just making a comment on the little circuit drawing on that page.
Sometimes, in Data Sheets, the author puts in an 'option' or 'suggested option' for an additional component with
dotted lines - just to show that it is an option and that it migth be a good idea to read any notes.
It's not some jargon fro anything fancy - it just makes reading easier.
Most people look at pictures, copy the circuit, but fail to read
(Including me).
I merely commented upon it as the resistor gets a mention in the text directly above the sketch.
Did you read it?
MOSFET Driver?
If you aren't doing really fast switching or PWM then I'd say that there was no need for it.
For your app I would have thought that an N channel MOSFET (logic level) would be fine for 'low-sided' switching i.e. between pump and ground.
If you are doing 'high-sided' switching with a P chan MOSFET i.e. between +Vpower and pump you may also need something simple like a transistor to pevent >5V getting to PICAXE output pin.
I'm not sure what you have decided upon. Either way is dead easy, but low-sided uses less components and is cheaper.
How's your electronics knowledge/experience?