Does the Avatar Logbook store unequipped skills

There are a few different colors on the map. @gorogoro got most of it right.

• White dots are completed story maps, and allow you to buy items from them, as long as a random encounter isn't there. If a Merchant is there, the selection is expanded the first time you shop there, with an item or two being on sale. The discount depends on the item (ie. Master Seals only get 9%, while Iron weapons can get close to 20%). You can also encounter random Risen battles here, and their difficulty is directly relative to what the story levels were. ie. A random encounter at Ylisse will be significantly easier than one encountered at Ferox Arena, or further in the story. If you fight a random battle at a spot that has both a Merchant and a Risen, the Merchant will be on the map. Saving them grants you a free random item.
• Red dots are the next story mission. There should only be one of these available at a time (unless the path splits, and I haven't reached that yet).
• The single purple dot is the DLC spot.
• Green dots are the Paralogue mission. These are extra, optional missions that you can choose to undertake, and get unlocked at certain points in the story. Essentially side quests. Some will reward you with extra characters (Paralogue 1 & 4), while some just expand the story, and provide extra experience and items.
• Orange dots are maps gained from SpotPass. These are added to specific areas on the map, and you have to be far enough in the story to challenge them. You can unlock them before you can challenge them, and they will sit there until you get far enough in the story. They seem to be extra missions, just like Paralogue ones, so they might reward you with the same things.

It doesn't change the story in any way but it does change the amount of enemies and the location of them on missions while making them significantly stronger and with different items + skills. The only way to get different storyline is to change your gender during another playthrough and have the characters marry different people. Please note that I haven't finished my Lunatic playthough but haven't seen any differences so far. Also, this is expected as the script writers had TONS of stuff to write already (most of which you will never be able to read), so this is most likely just a gameplay difficulty.

Spoiler: Lucina will have different dialogue with you if you are married to her throughout the game. You can also marry Chrom which will produce a slightly different story.