I am running my first 2nd ed campaign and have a question about the requirement of what psy powers you need before you can take the next. The RAW states: "To access a psychic power, the character must be able to trace a line along the paths of the tree from the top-most power down to the desired power without passing through a power he does not possess".

That to me suggests that you must have the powers in all paths between the root and the desired power, but it may be possible to create an unbroken chain without passing through a power the psyker does not own. My players are also split down the middle on this.

So in the case of Inferno, which has lines coming from both Molten Beam and Sunburst, is it sufficient to have Only Molten Beam, or would the psyker need to have both Molten Beam and Sunburst before purchasing Inferno?

I believe your former interpretation is correct; i.e. you could get Inferno having only purchased Manipulate Flame, Spont Combustion and Molten Beam.

You could also go Man.Flame - Spont.Comb. - Flame Breath - Sunburst - Inferno, avoiding Molten Breath.

If you wanted to limit the flexibility of Psykers somewhat, then requiring ALL connecting powers higher up the tree would be acceptable, but I think the default rule is ANY unbroken path.