Can I lace my hub with all inward or outward facing spoke heads?
The answer to "why alternate crossing spokes" is pretty much settled by the subtle suggestions from DanielHRicks and the direct and correct conclusions from the OP, in the very comments below the question.

The two remaining questions would be:


When is it possible to use non-alternating configurations, besides radial spokes?
In case of non-alternating configuration, should the spoke enter the flange holes inwards or outwards.


(I am, on purpose, not including the already much discussed pros and cons of using crossing vs radial.)

The first question is: there is also the SPIRAL configuration, shown in the picture below taken from the front wheel of my fixie:



(note the missing spoke at 2 o'clock...)

This spiral configuration is achieved when the spokes you have are too long for a radial lacing. Then you twist enough that they can fit. This is not so good, because it creates torsion in the hub's body, but I've seen that (and ridden that) a lot, and nothing terrible happened so far. Of course, it could not be safely used with disk brakes.

Now the good part: should the spoke run inwards (like the photo you posted and the photo I posted) or outwards? My answer would be: OUTWARDS, ALWAYS! I know that is pretty to see all those tiny spoke heads neatly arranged one beside the other in a pearl-collar-like pattern, BUT:


Outwards running spokes give a wider leverage to resist lateral forces. That means the same lateral force on the rim would cause a smaller variation in spoke tension.
It is a bit easier to insert spokes that run outwards (although in radial lacing it is not so important).
Most importantly: spokes running outwards touch the flange as they run to the rim, just above the elbow. That means the elbow is isolated from most of the flexion they would suffer whith the successive loading and unloading caused by wheel roll. This decreases fatigue significantly, hugely increasing the lifetime of the wheel.


So, the answer is your second option: All Outward (heads facing inward) Radial Lacing, UNLESS (!!!):


You use a hub for which the manufacturer forbids the use of radial lacing (most of them). Radial lacing might theoretically cause too much stress on the hub flange, since the force is applied in a direction where there is the least amount of material to resist the pull.
You use disk brakes (from previous answers, I think you're going to use those multi-mechano-power U-Brakes, so no problem).


(just for the record, the wheel in the photo I posted is opposite to what I am advising. That is because I already bought it that way. And I think the missing spoke - broke yesterday - has to do with this lame inward-running pattern.)

Hope this helps!