Go ahead and connect the miniature lights to the wire frame, as long as the lights have a tag on the string somewhere with the classic UL symbol on the string. Strings are cheap, so if yours isn't fairly new, go buy some.
As far as strings around the house, running a SINGLE extension cord from one outlet, then 3 or four strings end to end from that cord would be fine. Again, these strings are not expensive, and new ones have fuses in the plugs to protect you, the house, and the strings. If a fuse blows, you will know you have too many strings plugged in.
The first time I hang lights at a new house, I install brass cup hooks in the eaves, which is a real pain the first time, but every year after, installing the lights is a snap!