My first question is, are you suppose to build an item, or should I just buy the item without building it? (Ex. Buying Berserker's Greaves before buying Boots of Speed)

My second question is, can you build two different items from one item? (Ex. Building Heart of Gold and Aegis of the Legion from one Cloth Armor)

This is what I've been doing for Rammus:

1) Cloth Armor and Health Potion x 5.
2) Upgrade to Heart of Gold.
3) Get Boots of Speed.
4) Upgrade to Mercury's Treads or Ninja Tabi.
5) Build Aegis of the Legion.
6) Build Sunfire Cape.
7) Upgrade Heart of Gold to Randuin's Omen.
8) Build Guardian Angel.

I buy in this order:
Cloth Armor
Health Potion x 5
Boots of Speed
Ninja Tabi
Aegis of the Legion (do I build it from Cloth Armor?)
Sunfire Cape (should I buy Giant's Belt first?)
Randuin's Omen
Guardian Angel (do I build it from Cloth Armor?)

1) the upgraded items are all formed from base items, although there is always an upgrade cost. You can either buy it as a whole or piece by piece, it doesnt matter, although you migth as well buy the base items so that you have an advantage and finish the entire thing earlier.

2) no you cannot (sunfire cape requies chainmail anyway, not cloth armor)

So say, Item "A" cost 500g and is used to build Item "B", which cost 1000g. If I buy Item "A" first, Item "B" will cost 500g?

Yes, that's right.

Thanks

4) No Ninja Tabi
Consider 2 heart of golds instead of 1. And a banshee's veil sometime in that build