The pertinent rules are:

(1) A unit not ordered to move can be supported by a support order that only mentions its province. A unit that is ordered to hold, convoy, support, or not ordered at all can receive support in holding its position. For example, if the order is written “F Den S F Bal,” then the Fleet in Denmark will support the Fleet in the Baltic Sea as long as the Fleet in the Baltic is holding, convoying, or supporting. If the Fleet in the Baltic attempts to move, then the support from Denmark is invalid.

And...

(2) A unit ordered to move can only be supported by a support order that matches the move the unit is trying to make. For example, an Army in Bohemia is ordered to support an Army in Munich in its move to Silesia (A Boh S A Mun–Sil). However, the Army in Munich is ordered to move to Tyrolia instead (A Mun–Tyr). The support order fails because the move it’s supporting isn’t the move that was ordered. This support order doesn’t become a support order to hold.

Case 1:
Germany: A Bel-Lon.
Support of Bel Holding FAILS.

Clearly, A Bel ordered to London, and the support order does not meet the requirements of (2) above. The support order fails. Ruh simply is not adjacent to Lon, and thus it couldn't even support the Bel moving to Lon if it wanted to.

Case 2:
Germany: A Bel-Par.
Support of Bel Holding FAILS.

Same as case 1. Ruh could have supported Bel-Par, but it didn't do that.

Case 3:
A Bel-Naf
Support of Bel Holding FAILS.

Still nothing different here. Bel ordered to move. The support didn't match. CLEARLY fails per the rulebook (2) above.

Case 4:
A Bel-Neptune.

A Bel-Neptune is invalid.

Per the manual again,

Any vague or invalid orders are ignored.

This order is both not clear AND invalid, and thus it is ignored. The order is completely ignored. Later in the manual, we have:

Not giving a unit an order is interpreted as ordering it to hold.

Because Bel was not given an order (the only order given was ignored, thus it has no order) is ordered to hold. Since Bel Holds, Ruh S Bel is VALID.

Case 5:
A Bel-Bel

Not EXPLICITLY covered in the manual, but the manual does go to the extent to define that a MOVE order involves moving from one province to another, and it gives the example that an army in Paris could order to move to Pic, Bre, Bur, or Gas (not "move" to it's own space Paris).

Thus this order is simply invalid and the unit Holds.

Support for Bel Holds is VALID.

Case 6:
Germany: A Bel - no order received

Support for Bel Holds is DEFINITELY VALID.

Manual is clear that an unordered unit is by default ORDERED to HOLD. So supporting an unordered unit in place is perfectly valid.

That's my take! It is my opinions, but I don't see much room for debate on these they're all pretty clearly explained by the manual, aside from #5 which is clear only by similar example in the manual, not explicit statement.