How many items can the supply convoy hold

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.

You are right that DDG is short for Dodge. It's similar but different then Avoid.

Avoid is used to avoid/dodge Normal hits, like you stated correctly. With higher AVO you have a lower chance to get hit at all.

Dodge is used to avoid/dodge Critical hits. So with an increased Dodge, you have less chance to get critical hitted, while NOT reducing the chance to get hit at all.