yeah, we'll definitely talk about what effect the grid has on the game. As to different shapes, according to HPG's Tumblr post I linked in my last post, they originally tried a hex grid. I imagine that would make it hard to play a Ship between 2 adjacent Ponies.
If the points aren't awarded by a judge, you're left with winning by beating your opponents or completing objectives. Since TSSSF was specifically designed NOT to be head-to-head (again, see the Tumblr post), that leaves completing objectives. If all the objectives are present simultaneously, the game becomes very predictable, like chess with it standard openings. Having the objectives on rotating Goal cards keeps the game fresh, and difficult to plan around (again, because TSSSF is not head-to-head). If you want your victory points (achieved Goals) go down, you should play with Ithry's #MadeOurMark cards
Redrawing up to the hand limit keeps the game moving. The more cards you have, the more you can do. Also, it encourages players to get rid of (play) their "bad" cards. As to seven, I imagine the number was determined by trial and error, but I know that lets you make 3 plays, and hang on one Pony card.