How to SMS on iPad?
 

A lot of the instructions on setting up the prepaid data cards require SMSing.

How do I manage that on my iPad?

Is it possible to set up the card on another phone that has SMS and use it on the iPad?

The iPad does neither support SMS nor USSD (those *123#-styled codes by which you can check your balance etc.). For USSD there's at least an app called QueryUSSD which however requires your iPad to be jailbroken.
Say thanks to Apple for depriving your expensive device of such basic features. By the way they do this intentionally to make people unable subscribing to existing data tariffs but instead to enable providers offering special (more expensive) data tariffs for iPad owners.

So I guess the only options would be:

- do it on a phone, and transfer the sim
- have the store do it all

Of course, this is all kind of moot because AT&T say they're unable to lock it, and contrary to some reports on the net, my iPad 3g (original) wasn't sold unlocked.

(I've read iPad were sold unlocked, but my friends TMobile SIM is 'unauthorized' when I insert it and turn on the wireless services)

I guess I'll look into jailbreaking the thing...

Yes, using a phone would solve your issue. Just make sure you carry a microSIM-Adapter so you can use the microSIM in a regular phone.

Another workaround which would also solve your SIMlock problem would be to use a smartphone that supports WiFi tethering as WiFi hotspot so you could flawlessly activate your data option by USSD or SMS on the smartphone and share its internet connection with your iPad by WiFi.
Your observations made with that T-Mobile SIM indicates that your iPad indeed has a SIM- or netlock.

FWIW, I used my 1st gen iPad 3G with a TIM microSIM card in Italy in 2010 without any jailbreak (I still have the TIM SIM card I used and verified that it still works), so it may be an incompatibility with T-mobile and not a carrier lock issue. I do know that unlocked iPhones don't play well with the US T-mobile data services, so that might be the cause with your iPad as well.

What's the context between the iPad's missing SMS support and your use of an iPad in Italy two years ago?
What does T-Mobile have to do with this?
Btw the reason why iPhones don't play well on T-Mobile USA is that so far they simply don't support the 3G frequency band T-Mobile use for their 3G network (1700MHz), which they call "4G". However T-Mobile recently started refarming their 1900MHz spectrum and now more and more markets have 3G coverage on 1900MHz which lets iPhones "play well" on T-Mobile.

The context was that the OP mentioned that he could not get a T-mobile SIM card to work with his iPad and assumed that it was carrier locked-I was just offering my own experience with the same iPad model (which was carrier UNLOCKED for me without the need for a jailbreak, as is evidenced by my use of it with a TIM SIM card in Italy) in hope that it might help the OP with his iPad SIM problem-he may not need to jailbreak it, just use a carrier SIM other than T-mobile USA to verify its carrier lock status.