Ahh, what a thread to find, having just arrived home ready for a week’s break from teaching the violin 
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You’ve found a teacher, which is obviously a major step. In general, it’s best to let them demonstrate what to do (and not do) with the instrument. But a few things to start you off:
As you’re trying to tighten the strings, I presume the bridge is in place. It should be stood upright, in line with notches halfway down the ‘f-holes’ on the body of the instrument. If it’s out of line, you can ease it into a different position, gripping the bridge with both hands and steadying the instrument on your lap.
It’s not unusual for pegs to be temperamental - they’re wedge-shaped and held in by friction, so use pressure as you turn them. One thing to check is that the strings are would neatly onto them, preferably to the ‘peg handle’ side. This means the tension of the string helps pull the peg tight. In general, however, cheap violins use very tight metal strings (i.e. the cheap ones!), and screw-operated fine adjusters fitted at the bottom end of the string (the tailpiece) will be needed - have a look and see if they’re there.
One thing to check is the soundpost - this is a piece of dowel standing upright inside the body, visible through one of the f-holes. It’s generally not good practice to ship an violin with this in place, but this hardly matters with this level of instrument. Worth checking it’s there, though, because tension on the strings without the support of the soundpost can cause damage - and it’s a specialist job to reposition a soundpost.
The bow should be tightened so there’s a 1cm gap (‘little finger-width’ is the kids’ way to measure it) at the narrowest point - if the wood arches outwards, it’s far too tight! You’ve discovered the purpose of rosin: half-a-dozen strokes along the length of the bow each time you unpack the instrument is my rule-of-thumb.
And it’s worth checking the instrument is (approximately) the right size for Nature Girl. Place it on her left shoulder, extend that arm under the length of it, and if her fingers just about wraps around the end, it’s perfect. However, for a beginner, getting the exact size isn’t important, as long as it’s not ludicrously large.
I don’t know any websites of particular use. Every teacher will have their own preferred methods - I always use the Fiddle Time series. Children respond well to it, with even the easiest pieces being fun to play, often quite rhythmic rather than starting them off with comparitively-complex melodies (and with the CD accompaniment that comes with the books, they’re bearable for everyone else in the house.) You don’t mention how old Nature Girl is, but I’ve never have bothered with the ‘Starters’ book, nominally the first in the series, and even my most lesser-able (understatement!) 7-year-old pupils have always coped fine with a gentle introduction to ‘Joggers’, reinforced with lots of non-text & vocal work.
Have fun!