I have some advice:
1) You can stay in Peru AS LONG AS YOU WANT. Once your visa time runs out, they will only charge you $1 USD per day as a fine for overstaying your Visa. So an extra 3 months will only be $90 USD.
If any police officers catch you overstaying your visa, you may need to purchase them a coca cola or a ceviche dinner :) That is how things work here. I didn't create the system.
2) Lima is very nice in the summer, but in the winter it can be very dreary because it will be humid, damp, and cold. Also, you won't be able to see the sky for a couple months. Take day trips (and multi-day trips) to places outside of Lima, such as Paracas, and Ica.
3) Peruvians are FRIENDLY and WARM people, but watch out because a fair number of them like to engage in behaviors such as petty theft (waiters might charge you 6 soles for a 5 soles desert). This behavior will be most noticable in the following people: money changers, taxi drivers, and anyone working in tourism. This is politically incorrect to mention, but believe me it happens every day.
4) You should try all the peruvian foods, and as soon as possible. Lima is amazing for food. The peruvians will ask your opinion about their gastronomy, because this is a national point of pride.
5) The police men, policians and state officials are all horribly corrupt. I suspect Peru has a tunnel from the jails right into the government buildings.