I had GD, although managed it through diet and I wasn't on insulin.
During labour, which lasted for about 12 hours, I had to check my blood sugar (finger prick in the usual way) every four hours or so. Normally I would have done it however long after a meal (can't remember now as it seems so long ago!) and during labour I didn't eat the whole time so there weren't any meals to do it after, but it just had to be done regularly and the midwife who was monitoring me told me when to do it.
I could stop testing myself immediately after the birth - all over and done with! (You do have to go back for a follow-up GTT six weeks later to be sure that it really was GD and so you've come right now, as opposed to it being real diabetes that hasn't gone away after the birth.)
DD's blood sugar had to be tested three times in her first 12 hours. She was fine, but if your baby gets a result that isn't fine then it will be off to SCBU, insulin would be given and the testing would continue for however long is deemed necessary.
I would assume - but could be wrong as I wasn't on insulin - that you would continue to have it during labour at the same times that you would normally have it. Not sure what happens after the birth though, whether you'd be weaned off it or just stop immediately.
With regards to resuming a normal diet, yes, you can pretty much do what you like ... obviously within reason if you're BFing, since lots of sweets and things aren't great for BFing mothers, but like anyone could BF without stepping up the carbs! Seriously you will need those carbs to be able to feed! So yeah, GD doesn't restrict what you can eat anymore, but then what you can eat while BFing will become your main concern ... *sigh* ...