This is a tricky and a first one for me, I am well traveled but never with a kid. I need some help or just a second set of eyes to keep me in check.
I will be traveling with my wife and a 2 year old daughter. I cannot continue planning because it's kind of unknown with a kid. I am set on my dates, got flights and hotels booked. "All" that's left is the actual planing.

We arrive in Lima late on 9/2 (actually 9/3 at 1 AM), we are staying in Hilton's DoubleTree for 2 nights. 3 questions here:
1. Aside from withdrawing the money from an ATM, where in the airport should we exchange?
2. I assume that we ride from LIM to the hotel in a cab. Fixed price or metered? How much would it run us?
3. We will only have 1 full day in Lima and, from what I understand, everything is walking distance from the hotel. We mostly want to see major sights (no museums) and get some local food. Where should we go?

9/4 we are departing Lima for Cusco, we are staying in Tambo del Inka for 5 nights. 3 questions here:
1. The hotel had offered to pick us up for 220, which seemed very high to me. Is it worth it to rent a car or should we just get a cab at the airport or should we hire a driver before we leave? If it's the driver, please share the information if you have a name or a phone number. We might be using him for all 5 days. Also, we do not speak Spanish.
2. Machu Picchu planing. I was thinking of getting acclimated first couple of days, taking a Sacred Valley or Cusco tour (please suggest any), and then going up to Machu Picchu (no hikes, train there and back). Keeping my kid in mind, should I include a Huayna? Is 1 day sufficient to visit?
3. I will probably use the hotel to help me book Machu Picchu tickets to avoid the hustle with online purchase. But for everything else I'd like to avoid overpaying and keep the cost down. So, any good places to eat around the hotel? I am sure there are, just in your experience reasonably priced/budget restaurants.

I thought I've done my research but please chime in with anything and everything you can think of, especially if you think it will be difficult to do with a child. Thank you!