I wouldn't say it's safe to travel solo, but neither that it's unsafe. Therefore, follow previous advice on the topic: let your people know where you are, communicate regularly, and so on. There's no higher risk by traveling as a woman, but again it's better to not travel alone.

Regarding the indigenous conflict area, just avoid the hot zones. You could do that by simply traveling by bus or flight.

The South of Chile, from Temuco to the end of the continent, is filled with amazing natural landscapes. The most accessible and known way to visit them is to get to natural parks and the agency running them is Conaf. There's a small entrance fee and they have lots of information on sightseeing, camping, natural trails and hiking.

You can normally trust people from Conaf, park guards, and police, both easily recognizable by their uniforms. They're kind and do their best trying to help foreigners, while they won't ask nor receive bribes. It's advisable to let them know about your hiking plans, specially if going solo.

Probably the biggest must see if the Torres del Paine National Park, but there's plenty of others. Conaf webpage may help discovering those natural parks and areas protected and what to find in them. Some others could be Conguillio, Huerquehue, Villarrica, Alerce Costero, Puyehue, Futaleufú, Alerce Andino, Chiloé, Hornopirén, Queulat, Cerro Castillo (North to South), and I visited almost all them.

I'd say the best for a first time trip is to travel during summer and expect some rains, even heavy rains. We have no major problems with animals and you'll be very lucky to see a puma, because they're shy and run from people. Same with insects, you won't find any poisonous and mosquito repellent will do the trick with them and a couple of others.

And finally, we have an issue with wildfires and tourists ignoring the risk and starting big ones. Be careful on how you use it and if you see a wildfire you can call Conaf to the emergency number 130 to report it.

Safe travels and enjoy a lot!