Wow, you have been given some surprising information by the pros - not saying any of it is wrong, but it is a bit unusual.
First off, the P0420 is a code which indicates that the O2 sensor cross-checking is finding the cat to be performing below minimum spec. Now it's very common, especially for amatures like myself, to just hang on an upstream O2 sensor hoping that it's a bad sensor instead of the cat. That would be a much easier and less-expensive outcome. Sometimes it works and sometimes it doesn't. But I don't understand how the mechanic could know the problem is the O2 sensor without swapping it out. That being said, I would agree that the sensor is a good try, and would do that myself. This is a very easy DIY on our Aveos.

What the transmission guy said is even harder to understand. P0700 is the general transmission code, and it means that transmission-specific codes have been set and need to be read with a TCM reader. So if he did that and maybe also read the CVIs, then one would expect to hear about a transmission-related problem. But oil and coolant leaks? Are you sure this was a transmission shop?

I can't speculate on the rear seal leak, but I've eliminated oil pan leaks by just snugging up the bolts (not overly tight just snug). I can't imagine knowing it's a water pump leak unless the timing belt cover was removed and he could actually see water inside. Just a drip off the bottom lower timing belt cover could be coming from other places, in particular the plastic thermostat housing which is notorious for cracking. So you need to confirm for certain where that leak is coming from before messing around with the water pump (which is NOT a fast and easy DIY on the '06). You can try asking him specifically how he determined that the water pump was leaking. Do you know when the last timing belt change was done, and if the water pump was done at that time as well?

In addition to confirming the source of the coolant leak, you also need to get the P0700 diagnosed by someone who reads tranny codes - there will be one or more additional codes to evaluate once that is done. Good luck getting all of this sorted out!