Why do you keep going to that dealer? What happened to that AC shop you said you were going to go to?
It may be better to keep your AC problems in the same thread. You've started at least 5 different AC threads in the past few weeks and people don't have context for what the issues are without digging back at your posting history.
This could potentially be caused by the radiator fans not turning on when the AC is on. If you turn on the AC, do the radiator fans turn on and blow? They may not be on constantly, as they will cycle on and off as the compressor cycles on and off, but if the compressor is engaged, the fans should be running.
No. A broken recirculation damper will prevent you from switching between recirculation and fresh air, but will have no effect on AC temp, other than that you will get better cooling in recirculation mode, but it will cool either way.
If you want information on how to do things, there are two places I would look.
The first place is tsienna.net. There is a factory service manual (FSM) posted for a 2nd gen Sienna. This will have many sections that are similar, or even the same, as the 3rd gen. But to emphasize, it is for a 2nd gen Sienna, and not everything will be applicable to yours.
The second place is actually my first choice for DIY work. That is the official FSM which you can obtain at techinfo.toyota.com. You can get a 2-day, 1-month, or 1-year subscription. With any subscription, you can print out sections for later use. I will print-to-PDF and save PDFs of whatever sections I need for the project I'm working on, plus projects I intend to do. This results in a lot of clicking around, as each section must be downloaded separately, but it's the official repair info from Toyota.