Backpacking Lakes District in February

Yes, in February, the accomodation in tourist resorts is full, and also expensive. But if you're going to do multiday hikes, i guess you will camp.
It is possible to descend from Puyehue NP to Lake Rupanco and then continue to thr Termas (hot springs) de Callao, before returning by public boat on L. Rupanco then bus to Osorno (boats to Petrohue are too expensive).
You can do the complete Villarica NP traverse.
It is difficult to visit NP Conguillo by public transport, but Malalcahuello is an alternative, you can clilb volcan Lonquimay.

Most hiked are described on the wikiexplora website.

In Petrohue, just do the dayhike to Paso Desolacion.
Valdivia you just need 2 days or so to enjoy the coastline.
There are also many excellent treks further North towards Santiago in Central Chile. Think about it in case there is a spell of bad weather in the Lake District. From Chillan northwards excellent weather is almost 100% guaranteed. The top hike would be in Vilches, circuit of the Altos de Lircay reserve and the Decabezado Grande base camp. The Valle de Aguas Calientes, a short trek from Termas de Chillan, is also a top sight (many undeveloped hot springs in the middle of the mountains).

Ok thanks that's really helpful. By tourist resorts do you mean hostels? The lonely planet book lists a bunch of hostels that allow people to camp for less money- do even those fill up in February? Also how far in advance should I make bus arrangements

By tourist resorts, i mean places like Pucon or Puerto Varas, for any type of accomodation. Local busses either can't be booked or only a few hours beforehand. For the nightbusses Santiago Lake District , yes very exprnsive and full begin February, and even more so for the returns around end February, when all Chileans return to Santiago.

In hostels you would be competing with the hundreds of local university students who head south in February. But you can have better luck in less iconic places (with less night life). If stuck for a place, go to the local tourist office which often has a list of rooms in private homes. Chile has become more economical for Argentine tourists so there should be a lot of them around next summer, although they prefer January.

Will lesser visited towns like Entre Lagos, Petrohue, Villarica and Curacautin also be completely booked in February? And If I'm planning on staying in areas that will have full hostels how far in advance do you think I should plan to make arrangements?

To be honest, i never stay in Chile in February (but it is already difficult to find a room in Pucon in January). Towns like Puerto Montt have more availability. Most accomodation is in family run small places, named hostal, hospedaje, residencial, ... not in hostels aimed at foreigners (and generally more expensive).

OK thanks a lot. My last question is is any of the Villarica traverse technical and how reliable are the water sources along the way?

No not technical, excellent trek as long as you have good weather. On the eastern part of the traverse there is water, on the trail that goes round the Villarica volcano water is scarse, you have to get it from stagnant ponds at one point.