For starters, there is no way to ensure that the fish you breed will continue to have beautiful finnage or be "top notch" looking fish anymore. That's the risk you take by breeding them. If your desire is to keep the fish looking great, don;t breed them. If you want to pass their genes along so that you can create more that may have that look, you than can chose the pairs carefully to attain this.
Okay, to your questions:
#1- yes, you can breed a certain pair multiple times ( if the pair accepted each other the first time.) You will need to wait until both fish have been reconditioned before spawning them again however.
#2- you can't. As I mentioned, there is no way to guarantee a spawn and minimal damage. Thankfully, the fish is designed for a lot of punishment but the fins don;t always grow back in the same condition, foundation and coloring. That's the chances you take.
#3-The fry can be together for a long time however, at approx 5 months, when the males start getting sexually mature, they may start beating up on their brothers which makes it not advisable to wait that long. Also, Bettas have a hormone they can emit that causes their siblings to be growth stunted so it is important when raising the spawns that you do multiple water changes weekly to prevent any amount of this hormone from building up in the tank and stunting the fish. The good news is that if this does happen, by isolating the stunted fish in a different bowl or tank with clean water, they will start to grow again ( at least that's what I have found over the years.)
#4- I've bred males that were about 4-5 years old so as long as they are willing and able to blow a nest, they can be bred.
#5- I suggest you not try to do more than one pair in a tank at a time* so a divider is not necessary. What I do/did was to put the gravid female in a clear glass jar in the male's tank until she showed that she was ready to spawn. Once I saw her breeding colors, I would let her go in with the male. I do put some PVC pieces in the breeding tank so that if the male is not ready for her to be there, she has places to hide from the male while he prepares for spawning. As for keeping the 2 fish in the same tank post spawning, it usually doesn't work out. The male cares for the eggs and fry so the female is usually banished from the nest post spawn. If she doesn't get out of sight, males are known to kill their mates so that's not a good thing. Dividers will never be "air tight" so the fry will be able to go from side to side which is an invitation for the females to eat them so that's another no go. You are best to keep a tank or bowl for your females and your males so that the spawning tank is for initial fry raising only. Also, you can have a few hundred babies from one spawn so a 10 gal tank is not nearly large enough to grow out the fry. It's not due to the gallonage, it's the floor space. You need space for the fry to grow. I usually breed the fish in small shoe boxes or tanks or bowls or whatever and transfer the fry to long, wide flats or tanks to grow. If you only have the one tank, I suggest this is not a good setup for doing this ATM.
*- I put this here because it is possible for a male to do multiple simultaneous spawning with 2 or 3 females but in order for this to happen, you need a large tank with multiple areas for the fish to interact separately from each other. I also believe the hatch ratio goes down with multiple simultaneous spawnings but I can't locate the article this info came from so it may not be accurate in all cases.
You can see some of my breeding setups in the albums section of my profile. You will also see pics of a female in "color" as well as a pic of the flats I used to grow out the fish. If you still have questions, shoot me a PM or ask on this thread.
Hope this helps