I've seen some sheet music like this before, brought to me by guitar pupils from Hong Kong. The cross-headed notes are quite easy to get your head around; they simply show you which strings to pick while using the chords above the TAB stave, and the rhythm of these arpeggiated notes. The arrows show how many strings to strum for the chords above the TAB stave.
As for the numbers below the guitar TAB, these show you the notes of the vocal melody (or instrumental melody in the intro). But, instead of using actual pitch names or notes, these numbers represent the degrees of the scale of the key you're in. So, in G Major, a 3 represents a B natural, a 2 represents an A natural, and so on. It's a bit like the movable do system. This is why you have the marking 1=G at the beginning.
ADDITIONAL INFO: obviously, this Solfege method of showing the melody line with numbers, doesn't give any information about which octave notes are in. To get round this, dots are used: a dot above a number shows that a note is in a higher octave; no dot indicates a note in a middle octave; a dot below a note shows that a note is in a lower octave. Although this is not quite as accurate as conventional notation, it works pretty well; it is unlikely that a vocal melody would have a range of more than 3 octaves (unless you're notating some Kate Bush, perhaps...)
Quavers and semi-quaver rhythms are shown with the appropriate beam lines under the melody numbers. Rests are indicated by a dash.
It's a really different system to the one I'm used to!
EDIT: @Dom added a link to this Wikipedia page, about this kind of notation, in an answer to another question recently. It has some useful info...