Hey there, welcome to the forum and wonderful world of betta keeping! :)
Sounds like you've already discovered what wonderful and fantastic little pets these guys can be! Beware! They're also VERY addicting....almost like potato chips, you can't ever have just one! ;)
Haha, anyway....to answer your questions...
A 1 gallon is pretty small. Alright for a temp home, QT, or in special cases a heavy finned male or disabled fish....but IMO/E for most normal healthy bettas that extra 1/1.5 gallons even really does make a difference.
Personally, I would recommend an upgrade in he near future...if you go with something 2-3 gallons you could probably sill fit it on your desk. For the most part, the footprints of most of those tanks aren't too much larger.
For water changes....a 1 gallon is going to get dirty and start building up harmful ammonia quickly, so based on my own experience I would recommend three water changes per week; 2 50-70%s and 1 100% as regular maintenance.
Honestly, I would recommend a heater.....unless the room you keep him in stays in the low/mid-80s at least(water is always a little cooler then room temp)and fluctuates no more then a couple degrees day-night/seasonally then you need a heater, if only to keep the water at a stable temperature as frequent fluctuations of more then a couple degrees can be stressful.
You want to keep the water at at the very least 76 degrees F, but 78-81 is a little more ideal. I would suggest a good adjustable heater, those present and 'pad' like heaters tend to be unreliable and often under/over heat your tank.
A good adjustable 25 watt heater will get you up to 5 gallons when you decide to upgrade, though those can be difficult to locate in stores sadly so you may need to order online. Hydor THEOs you can get on Amazon, I've heard nothing but wonderful things about them. I do believe here is also The Elite 50 watt, which states its a present heater but I've heard is actually adjustable, and is really no different from their 25 watt(which last I checked they had stopped selling)on Amazon also....I haven't checked recently though, so I'm not sure.
As for food...TetraBetta is really quite a low-quality pellet, lots of all kinds of fillers in there. I would recommend picking up a higher quality pellet like New Life Spectrum Betta(or Small Fish)Formula which has more meats and meaty proteins, which is much better for a carnivorous fish like a betta. It also includes garlic(which is one of my favorite things about it), which entices the appetite and I believe also has some anti-parasitic properties.
Here is a nice little thread that explains a little better what to look for in a commercial pellet food(they use Omega One as an example, but there has been a lot of controversy over the brand lately so I'm hesitant to recommend it): http://www.bettafish.com/showthread....99#post1263699
With NLS pellets, I would suggest feeding 3-4 pellets twice per day, supplementing a meal 1-3 times a week with frozen foods like brine shrimp and blood worms for a little variety. If you can get your hands on some live foods, like mosquito larvae, blood worms, brine shrimp, or even flightless fruit flies those would also be good to feed as well.
Nah, don't feel bad for destroying his nest.....hes not really going to miss it, lol. Nesting an instinctual behavior, just something they do when they're at the age to breed. Probably after you destroy it, he'll make another one anyway....though if he doesn't don't be alarmed. Its all about the personality of the fish, some nest all the time, some never nest....and some nest a few times and then stop. Just depends on the fish. ;)
In the exercise/flaring department....that all sounds find to me, both your schedule, and how he flares. Individual personality plays a part here too....some bettas are a lot more enthusiastic about flaring and the mirror then others, some will only flare a certain objects....and some could care less about flaring period. It just depends is all. ;)
Also, since you don't have a heater, hes probably a little cold and not quite as enthusiastic. It might change once you get him a heater. ;)
Lets see....I think I covered everything...xD Hope I could help! Good luck! And I adore your guys name by he way. ;)