I'm going to assume you grew this from seed and not a clone or already rooted plant that someone gave you. Are they auto or photoperiod seeds?
So my 1st question is, since i have my grows in 1 gallon fabric pots, do I need to replant them in larger pots (currently in the veg state) or can I complete my grow in the same container size that I started them in?
When you say "grows" are you referring to more than one plant in a pot? Did you germinate the seeds in the soil by planting them all in one pot? If they are multiple seeds than you will need to carefully remove them from the pot, remove the dirt around the roots being careful not to damage the roots and replant each one in their own pot. Without a picture I can't tell what "Going well" means.
Because I don't have a visual of the plant(s) I have to assume, going by your "going well" statement, that they are mature enough to be planted separately. I would plant them in 1 gallon pots and grow them as large as you need before they flower if auto or you induce them to flower if they are photoperiods.
If it's just one plant in the pot then, yes, it would be a good idea to up pot them but that also depends on the size plant you want. This pertains to photoperiods as they aren't finicky about transplanting like the autos are. If it's an auto I would keep it where it's at and let it do it's thing but next time, if you're doing autos, I would plant them in a 3 gal container so that you don't have to transplant or be limited to a one gallon pot.
2nd, once i have completed my grow and cut all the buds off to dry, is the remaining stock of the plant done, or can i regrow from the same stock?
You can regrow but I would advise against it. Some have and do do it but I prefer to just chop the entire plant down and start from scratch.
3rd, Once my grow is complete, can I reuse the same pots and soil or do they need to start from scratch again?
Yes on both. In fact, I would say it is beneficial to reuse the soil you've already used as it will now contain a lot of the bacterial endophytes and fungi that the plant likes. You can use a product like Recharge to recharge the soil nutrition but I just take the soil I grew in and mix in about half of what I have in used soil with new. Haven't had an issue yet. The one caution I would say is by not using new soil, the soil buffers may be depleted so if you're not pHing your feed solutions you MIGHT run into a pH issue.
When you get a chance read this. I posted it so that newbs like yourself can get a leg up on how to choose the right pot size for the media you want to use along with what's going on in the soil when you water and how to water properly.
Watering cannabis explained by Aqua Man - GrowWeedEasy.com Cannabis Growing Forum​