The Player's Guide Says...
Do you extend one row and column, check to see if the figure fits, and if the figure doesn't fit you treat terrain as clear or do you iterate on extending the starting area?

You continue extending starting areas until you reach a maximum of half the map their starting area and half the map yours since your opponent equally extends starting area as much as you do. If you still cannot fit the multibase figure you ignore terrain on the initial placement and it reverts after the figure moves off it. I'm not 100% on that but i'm fairly sure that's how it works for multibases. I know that you keep iterating extension for forces too large for the starting area.

Looks right to me. Try expanding the starting area first, if that cannot be done to successfully make a space then ignore the problem terrain for placement.

I've been told from time to time that after expanding your starting area, if your larger character and the rest of your force CAN fit somewhere you have to stop expanding and they MUST fit in those squares even if it wouldn't be the best places, in your mind, to put these characters at the beginning of the game. Would this be accurate to the rules?

But how much do you have to expande you starting area before deciding to apply the second chance (ignore initial terrain and elevations)?

I see important to define which one the ultimate starting area is when using maps like Hawkworld or Rooftops of Gotham with special rules that place characters in those squares; the original one , the expanded one or the expanded-cleared area?

You would expand yours and your opponents 1 column/row at a time. This will continue up untill there is no room because they would overlap. Starting areas cannot ovaerlap. Then if the character can still not fit, you go back to normal size starting areas and do the same only ignoring terrain for placement.

This is correct, and I have never seen an instance of it not working (where the team/figure couldnt be made to fit) unless we are talking 5000 point swarm teams.

OK, so the new expanded area is considered the starting area when play those maps, isn't it? You could place your characters in any square of it, not only on the purple ones.

Correct, characters that have special powers/abilities that work when in starting areas will work anywhere in the new starting area, not just the purple.

Lean Harper/Cypher swarms work great againt those that play Mystics far to much.

Don't forget Big Figure.

Correct. You are only allowed to expand the starting area to obtain a legal placement, not an advantageous one.

Both players play Galactus. The first player (foolishly) picks Realm of Death. Only one half of that map has enough room to place a 3x6 character.

Until you ignore terrain, then both Galactuses can start adjacent in the middle of the Realm of Death, punching like walls don't even exist

No, once you cannot fit characters normally to the point where you need to use the rule to ignore terrain, you starting area shrinks back down to normal size and then only extends to accommodate those that wont fit in the starting area then.

So the only way that would be possible with Galactus is if you have that many extra characters on your team to do so.