Hi “RR75” (?):
I hope that you don’t take offense at this - it is meant with the best of wishes, and after all, you did ask for advice. I hope other new players will find it useful if a bit didactic…
First of all, since you took delivery of a new set in “early January”, and today is the first day of February, I would say first and foremost that you are getting way ahead of yourself. Rolls after three weeks??? No way. You should be practicing bag and bellows technique and playing long, steady notes for the first weeks - no tunes at all. Leo Rowsome’s suggested schedule for learners years back included exercises and scales for the first couple of years. The only reason for even considering a simple tune at this stage is to keep yourself from succumbing totally to boredom. And face it, if you are getting impatient at this stage, there’s little hope for you, barring some kind of conversion experience. The pipes will teach you patience if nothing else!
My suggestion for an adult would be that bag and bellows technique, if you are to get it right and avoid bad habits, will preoccupy you for the first month or so. The D and eventually G scales, properly practiced with both legato and stacatto technique, will take weeks more, and should continue to be practiced for the first year. You can think about a simple ‘song air’ (as opposed to a “slow air” - a term usually reserved for advanced playing of songs in Irish) like Eileen Aroon [Eibhlín a Ruin] or the West Wind, around the second month. Getting that to sound like music will give you plenty to do!
Especially coming from outside the tradition as you are (and as I did), it’s vital that you listen a lot to good piping - and not just piping, Irish traditional music in general. Avoid highly produced, “exciting” commercial stuff played fast - better is some moderately paced, tasteful stuff. Put it on your iPod or mp3 player or victrola or whatever, and listen to it every day. Do you drive? Listen to it in the car too.
I take it that you are an adult - or at least over 15 or so. One can learn pipes as an adult and make progress (I did), but it takes longer.
OK, now for the satisfaction of your curiousity, yes the Clarke roll directions are correct, and whatever anybody else wants to call them, in Irish piping we generally call them “rolls”. Their rhythm is unlike classical music’s rolls or turns (which you can learn from listening); they are composed of a long-ish note, such as F#, and two motions which we call the ‘cut’ and the ‘pat’ - the cut being a quick lift of an upper finger (in this case the A finger), and the pat being a quick ‘patting’ motion of one or two lower fingers (in this case the F# finger itself). There are in fact several types of F# roll, as mukade infers, but you should not infer from what he said that “anything goes” - there are in fact very definite aspects to each flavor of F# roll. In short, there are many correct ways to play them, and an infinite number of incorrect ways… listen to them, but for now, don’t try to play them.
I would strongly recommend working on cuts for a good while before thinking about rolls. It will take a good bit of time for you to achieve nice clean cuts on each note. Try to get your cuts to sound like the ones on the Clarke tape/CD (I do hope you have the CD!).
The Clarke book is excellent IMO. But getting all the way through it should take years for most adults - you can’t just move on to a new lesson each day! Or even each week, unless you are a true genius and are spending hours a day practicing. In which case you’ll probably injure yourself - easy to do with these, if you don’t have good tuition.
You live in a challenging environment for piping - reeds hate dry weather, and you are not near any reedmakers who can help - you are also a long way from the epicentre of piping. There are some learners in your area who may be able to help; but bear in mind that they are isolated too, so try to do a sanity check on advice you are given. Get yourself to a tionól or pipers’ gathering, preferably a major one with a high standard of piping, as soon and often as possible.
In the meantime, I’d suggest joining NPU (http://www.pipers.ie) - it will give you access to videos, recordings, and tutorials of fine pipers among other benefits. If you start with some of the simple tutorials there, you can ask for information in their forum or this one - at least we’ll be sure to be talking about the same things.
Of course the other important thing is to have fun, and I’m glad to hear that you’re having fun. Might as well get off to the right start, it will lead to even more fun in the future.
Did I mention listening ? 
good luck and best regards,
Bill