1. Should I go with light or heavy armor? I keep going back and forth on it. Heavy offers better protection, but light is lighter and fits better aesthetically (imo, of course).
As per definition (in TES atleast) a battlemage should use heavy armor. But whatever, it's up to you to roleplay whatever you want. Skyrim's light armors are sturdy enough to warrant use by a battlemage anyhow.
2. Is it even worthwhile using a shield since I'll probably spend most of my time running backwards shooting fire at people and then running in for the kill?
When you play a battlemage it's probably much more usefull to ditch the shield and use the free hand to ready spells. That way it's more easy to combine melee and magic during battles, which is off course what a battlemage does.
Though
"running backwards shooting fire at people and then running in for the kill" isn't really strictly battlemage behaviour, and it would become very repetitive fast imho. You'll have more fun combating enemies combining magic and melee simultaniously depending on the situation you find yourself in. Casting drains, weaknesses, conjurations, destruction spells, while dealing deathly blows while you're at it. Altenate a bit between ways of battling, experiment and change your combat behaviour depending on your situation. Battlemages are versatile and they can be a lot of fun to play, when played right they can give you pretty immersive alternating gameplay.
2b. I've never really used Wards much, do they block phys and magic damage or just magic?
Wards are restoration spells. So a battlemage wouldn't necessarily have them in his/her skill set. But again, that's up to you. You may prefer destruction or conjuration spells over wards anyhow, because the added protection of casting a ward is less usefull since you're already protected by (enchanted) armor.
Wards act as magical shields. They give extra magic resistance and they boost armor. So they can decrease physical damage as well as decrease magical damage, but it's dependant on the type of ward you're casting.
3. I plan on my main spell trees being Destruction (I have Balanced Magic), Conjuration (I plan on using bound weapons, and summons are always good), and Alteration, and also using Restoration when necessary. I'm particularly curious about Alteration, is there more to it than just increasing your armor? Is it even worthwhile at all?
Though alteration in Skyrim seems somewhat focussed on increasing protection, it does have some more uses besides that. Just read the http://elderscrolls.wikia.com/wiki/Alteration_%28Skyrim%29 on it.
Waterbreathing, telekinesis, "light" spells, paralysis, "detect" spells, and off course spells and perks to increase protection / absorb, they're all pretty usefull. But yeah, conjuration and destruction are of more use if you wish to deal damage.