Let's take the crashing first. It is unfortunately common for Mac simmers to experience crashing. There are a couple of things you can try to avoid this from happening. There are details in the thread that Crinrict linked to, so have a careful read through that. However, to summarise, these are the things that I do that seem to prevent my TS3 game crashing on my iMac (I am using Mavericks OS too).
1. Before you go into CAS, go into Edit Town, or try to save the game, first put the game into windowed mode (press cmd-return). This means that if the game crashes, you can use the Force Quit option to close it down rather than crashing your whole Mac.
2. Purge your RAM. If you don't know how to do this, check out BluebellFlora's guide, which has been updated with Mavericks-specific instructions. Purging RAM makes a big difference and has mostly eliminated crashing for my game. The link is: http://bluebellflora.com/the-sims-3-on-a-mac/resetting-ram-during-gameplay/
If you have Activity Monitor open and then open the Launcher, you will probably notice that TS3 immediately hogs a load of RAM (the "used" memory number will go up). I let the Launcher appear and then open Terminal and purge the RAM. Then start the game up, go into windowed mode and take another look at Activity Monitor. If the amount of free memory is low, purge in Terminal again. You can either keep the game in windowed mode, or, if you are like me and enjoy playing full-screen, go into windowed mode occasionally to check the RAM and purge.
3. Always use Save and then Quit rather than the combined Save & Quit option. I find it freezes up more readily when using Save & Quit. I save quite often (maybe twice per sim day and always before going into CAS). Use windowed mode while saving (this is also a good time to check Activity Monitor).
4. Patch through to the latest update. The ITF update include Mac fixes that did actually work. If you haven't patched yet I would recommend doing so.
5. I would recommend trying the the tips in the "Primary things to try first" section of the link that Crin gave - particularly moving The Sims 3 folder out of documents and letting the game generate a new one. Then you can see how the game works with a fresh folder (and use the purging of RAM too) and just see if you can play for a while before adding back any old saves or downloads that may include corrupted or problematic content.
Regarding Ambitions not installing properly, is this from a DVD or digital download from Origin? If you only have the base game and Ambitions, it would not take long to do a clean installation. To make sure it is clean, read this first: http://bluebellflora.com/the-sims-3-on-a-mac/how-to-do-a-clean-uninstall-and-reinstall-on-a-mac/
Let us know how you get on.
Also I forgot to mention that you might want to turn down some graphics settings. I have a lot of them on medium rather than high, and my game still looks nice.
