I saw a recent post about a generation lmit? What happens when you get to thirty? I am pretty close, on my twenty-third, I think. I don't want to have to start over, because I have 42 collectibles, and 96 trophies!

Unfortunately, the same issue that affects the desktop versions of the game, also affects the iPhone/iPod touch version. More information can be found on this situation here.

Thanks. Will I not be able to pass on the house anymore?

When you reach the 30th generation, you may wish to pause the game in order to save your family. The thread I linked to above has situations where other players have attempted to pass on the house, and the results they had while doing so