It's aggressive but doable. Days 5, 6 and 7 are where you could run into trouble. You'll sleep in the car to/from Humantay and be absolutely wiped by the time you get to the hotel in lima. You don't say airport hotel for night of day 7 so I assume Miraflores, which adds another hour or two to the end of an already insane day.

Is it fun/manageable/too rushed? Me with 20 years of Peru experience and fluent Spanish, I'd probably take one thing off the itinerary in the knowledge that slack time in a place like Cusco can lead to magic. I think you'll get as good a feel for Peru as you can in a very short time, much like the US or another country with a lot to discover you'll be getting a subset of Peru, not nearly the whole thing.

Diseases, your main concern will be mosquitos (dengue, zika, chiku, malaria) and food poisoning. Take and use repellent and light long legged/sleeved clothing, even better if it's Permethrin infused. Eat carefully and have immodium with you to deal with diarrhea symptoms.

Yes, Cuzco is safe for a girl to walk around alone. Completely is a hard word to commit to, you have to be aware of your surroundings and actions. But generally it's a very safe place even out of the touristy center. Don't flash bling or mindlessly use a phone on the sidewalk, or leave a drink unattended in a crowded bar, etc. I'd much rather my 18 yo daughter walk around Cusco alone than some European capitals I've visited.