I had to add spoiler tags to a few items in your post, Katesmom. A few of the things you mentioned were a bit spoilery
I don't know that they even planned to include so many scenes with Tywin and Arya together from the beginning. I'd guess that they saw how really great Maisie Williams and Charles Dance are and decided to add those scenes. Those scenes are one of the good byproducts of book characters being eliminated from the show....and as a huge fan of the books, I don't think there aren't many of those! I think they've done a great job of adding some of the expository info from the books - although there's A LOT more they could add - without it feeling awkward. Of course Arya would admire Rhaenys Targeryen.
I don't think Tywin is much of a presence in book 2, but Charles Dance is so fantastic. The first scene we ever saw him in - the one where he skins that animal (deer? elk?) while lecturing Jaime - is SO powerful and compelling, even though, yuck, skinning an animal. It so completely captured who Tywin is.
Jaime! I so missed him. He's deliciously bad. That "Dead Ned" line was vicious and great! I loved his little bit about how it's a good thing he was born who he is because he can't do anything else. Even while he's tied to a post and sitting in his own, well, you know, he's still the same Jaime.
I'm okay with the producers making small changes to the books, as long as they don't change the fates of major characters by killing them off or NOT killing them. We've had some minor characters die on the show who live on in the books - the blood rider than Khal Drogo killed in season 1 and Dany's handmaiden who died last week are two - but none of that really affects major plot lines. I just don't want to see them kill someone MAJOR who lives in the books just to keep book readers on their toes OR save someone who dies for the same (or any) reason.
I think even people who were upset when Ned, Drogo or Robert (or all three) died can see now that those deaths were necessary to propel the other characters along. I'm hopeful that GRRM's involvement in the series will keep the producers from changing the plot too much.