I believe he is capable of love, but he is a very guarded man because of Joanna's death. Outward shows of affection aren't going to come out much in public. In a situation like that tho, there's no way in hell Tywin wouldn't comfort his grandson. Plus, in the long run this is his opportunity to draw Tommen to him and guide him. He might as well start by being their for the boy right after he had to watch his older brother die in a pretty terrifying way.
Yeah. I wonder, given how things turned out with Joffrey, if all the Lannisters, including Cersei, would consider doing things differently with Tommen to try and prevent another Joffrey from happening. Just doing the opposite of whatever the hell they did in raising him, just out of gut reaction to not head down the same path as his older brother.
And if anyone would want that more, it might be Tywin. It's kind of amazing looking back at the number of times Tywin must have wanted to slap that kid out of the sheer stupid and embarrassing things he'd done.
I don't agree with that. This same man had the only woman who truly loved his son raped by over a hundred men and forced said son (who was only 16 at the time) to participate in the event. He sees his daughter as a vessel to produce more political connections, and disowns his "Favourite" the moment he disobeys him. We've never seen him show affection towards anyone or treat his grandchildren as anything more than as tools to further the Lannister dynasty. Even Tywin's biggest defender, his sister Genna says that whatever was good in the man died with Joanna.
I think the show presents a greatly idealized version of Tywin, mostly because of Charles Dance being so magnetic.
I thought she was paid for her work? I don't believe she was raped, but that Tywin made her a very rich woman for every single man that she took infront of Tyrion. From what I know of Tywin via the show, and the books (I'm in the middle of the second), he's a stubborn man. A man who believes that when he's right, he's right. With him, it seems to me that the ends justify the means. A hard man who believe those things is going to be a dick, but I can understand his motivation. He's also very protective of his family's integrity. Tyrion, despite not being his favorite, is still his son. His son loving, and marrying, a prostitute is just unbecoming in this society. And it's sad, but Tywin proved his point about that girl Tyrion loved. I think it's something that even someone like Ned Stark would have forbidden of his sons, though the wouldn't have done it in the same manner.
The use of children being political tools through organized marriages is just another byproduct of the world they live in. Ned's marriage was a political move, Robb being betrothed to a Frey was political, Margery with Joffrey was political. The only one I can think of that wasn't a politically motivated marriage was Robb's, really.
No, he hasn't. The last book to be published was A Dance With Dragons, which is the fifth one, back in 2011. The 6th is supposed to be published around these days (years). So we gotta looooong way to go yet.
In terms of chronology
1996 - A Game of Thrones
1998 - A Clash of Kings
2000 - A Storm of Swords
2005 - A Feast for Crows
2011 - A Dance with Dragons
2017 - The Winds of Winter
2069 - A Dream of Spring
If I were you, i wouldn't read book 3 now. You best watch this season without knowing anything that will happen at all.
I suggest you read the first two. And when this season ends, you pick up book 3.
Wow, the first few are alot closer to eachother than I would have thought. The first three were two years apart. And those books are dense, with well packed lettering (no large fonts to extend page counts). I thought they'd been longer waits, but damn if the jump from two years to five, then to six, seems...odd. Though, I guess his workload did increases. He's written other books, in between, I'm sure.
For anyone whose thinking about reading the books, I say jump in. They're lengthy reads, and add a nice insight into what you're watching onscreen. So far, a quarter into ACOK, I've gotten a better grasp on some characters and motivations. Stannis, for example, I found to be much more relatable.
Who on the show will i now love to hate? 
I would have lost it!
