Peru in 9 days - Safety Concerns and itinerary review

We did Peru years ago with the help of Lima Tours. Google them and see if you like any of what they offer in the places you want to visit.

The train back to Cusco will be crowded if you go on season. I can’t say anything about staying with families at the lake as that is not what we would like to do.
There is crime everywhere in the world so I would not be out late in any deserted place.
We did get sick so be careful with what you eat or drink.
Llamas are not everywhere.
Have you done any research at all about day tours?

Have you read Lonely Planet? I think they're a great planning resource for lodging and tour recommendations. I don't think alpacas are aggressive, they are domesticated and used for transport, wool, etc. I doubt poor Peruvians would have pets (as pets are a luxury and require resources) but you'll likely see guinea pigs (they're food too, unfortunately) and stray dogs milling around, and of course alpacas. Most stray dogs are mellow (of course I can't speak for every one of them, I guess I would say watch out for packs of dogs based on their behavior). Just stay out of desolate areas and you should be fine. Many people, including women, travel to Peru alone and have no issues. Obviously, if you speak at least some Spanish, that's a major plus.

I enjoyed a portion of your itinerary (July 2 - 6) several years ago. It was combined with travel to Bolivia and Ecuador in just under four weeks. I felt safe and welcomed in all three countries. I completed the Peru excursion that you’ve outlined in April just as the crowds were beginning. My biggest challenge was acclimating to the higher and changing altitudes, especially in Bolivia. My access to Lake Titicaca was via Bolivia so I can’t comment on that question. Animal behavior everywhere but specifically llamas roaming was never an issue. We even visited a llama farm to learn more about them. I can’t address the MP guide question because our group was traveling with a tour guide who arranged everything. However your departure time would depend on the bus schedule. Our group took the first bus that morning. Following an afternoon visit to MP, the early morning trip back up to MP was a highlight for many. It was worth it to leave Aguas Calientes as soon as possible afterwards. Our train car was full of MP tourists for a good portion of the journey.

Dollars were in high demand everywhere in Peru back then. I don’t what is preferred these days.

Initially I was quite worried about taking this trip, even canceling due to safety concerns. Finally I went and had an outstanding time.

Here is a link to CDC guidelines regarding health and safety - https://wwwnc.cdc.gov/travel/destinations/traveler/none/peru

Though I've made several trips to Peru, I made only one visit to Cusco and Machu Picchu, and that was back in 2012. However, I do not recall seeing llamas, or any other sort of animal, just roaming around; and in fact the only llamas I recall seeing in Cusco -- and there were very few -- were sitting tamely beside their owners, invariably young girls in colorful traditional costumes, waiting for tourists to pay to take cute photos.
You do not have to worry at all about safety on the train to or from Machu Picchu, at any time. This is a dedicated tourist train. Only tourists ride it; I would be surprised if more than a few locals could afford it. Peru tourism depends on Machu Picchu, which in turn depends on this train -- they're not going to let anything happen to the passengers.
As to where to stay in Lima: Personally, I favor the historic center, and I've found it to be much safer than many people think; but realistically, I know that the vast majority of tourists prefer fun, modern, familiar Miraflores, and I'm sure you will prefer it, too.
As to what to do in Lima: since you have allotted only a half day, this is hard to answer. On any of my trips I could easily have spent a week in this fascinating city, and though I have never had the vacation time to do so, I think I came close once or twice. But if you do stay in Miraflores, here are a couple of easy suggestions: [1] The ancient site of Huaca Pucllana, right in the middle of Miraflores. (They do have a few llamas in a fenced-off section of their garden area, but you can easily avoid that part of the site.) [2] The malecon, or oceanside walkway, and in particular the Park of Love. The outrageous "kiss statue" alone is worth the walk!
Finally, I believe you'll find more opportunities to use your credit card than you think, but in Peru it's always a good idea to have cash on hand in crafts markets, or smaller shops and cafes.

We were in Peru in April of 2019. Half of our time was spent on a tour and the hotel was in the Miraflores area. There was lots to walk to as noted by Faedus. After the tour we spent 2 nights in an Airbnb near Plaza San Martin. The area was a bit gritty but we felt safe.

We had no issues with llamas. Any llamas we saw didn't seem to be that interested in us.

We used cash machines several times in various towns to have some soles to carry. We made the mistake of getting some soles from a machine at the airport that had high fees. I don't remember having any issues using credit cards at hotels or for meals.

You haven't left much time for elevation acclimatization, if you can move on (lower elevation) from Cuzco on arrival and visit there on way back. The Lima airport is a solid hour from City center with traffic. The city is very spread out. With essentially a half day and not much interest in the city I'd suggest not bothering with it. Get an airport hotel or a connecting flight to Cuzco right away. As for immunizations you probably won't find them at Walgreens. The CDC website has a way to search for local providers. Since you're really close to your trip date you might be a bit too late to have full immunity but a medical professional can help you. Safety wise I felt mostly safe but I speak some Spanish - do not expect English speakers except in tourist areas. Good luck and enjoy I loved my visit there.

We love Peru and have visited it three times.
The last time we did a great four day tour of Cusco, the Sacred Valley and Machu Picchu with PeruAgency.com

Cost in 2019 was $799 per person for a PRIVATE tour with lodging, transportation (except airfare from Lima to Cusco) and most meals. Guides were university educated and wonderful.

As for safety, Miraflores is an upscale neighborhood and safe. The area around the airport is not so good, be careful there.

Llamas and Alpacas (people there treat them like pets) seem harmless, but just don't push your luck and aggravate one.

The wonderful glass top train doesn't go all the way from Cusco to MP. Also, there is much to see between those places.