Tell size category of an object

Yes.

The soulknife ability clearly states that if a soulknife has Powerful build the knife it manifests is larger to match the ability. So you would deal increased damage due to having a larger knife than say.. a regular human.

By design this also means if you can find a way to get Enlarge Person to increase your size, then you would also benefit from the soulknife damage increase granted by powerful build as well.

Form Soul blade states:

A soulknife must choose the form of her mind blade at 1st level. She can either form it into a light weapon, a one-handed weapon, or a two-handed weapon. Once chosen, her mind blade stays in this form every time the soulknife forms her mind blade. The light weapon deals 1d6 points of damage, the one-handed weapon deals 1d8 points of damage, and the two-handed weapon deals 2d6 points of damage. All damages are based on a Medium-sized creature wielding Medium-sized weapons.

This constrains the Soul blade to a certain type of weapon, such as longsword, shortsword, trident, etc. Whichever you choose when you first manifest it. The size changes based on your own size, which may have variable scaling.

Your Reasoning is Correct...

... from a Rules as Written perspective:

Forcecage reads:

A prison in the shape of a cage can be up to 20 ft. on a side ... A prison in the shape of a box can be up to 10 ft. on a side ... Any creature that is completely inside the cage's area is trapped. [Emphasis mine]

The note on space (pg. 191) reads:

A creature's space is the area it effectively controls in combat, not an expression of its physical size. A typical medium creature isn't 5 feet wide. [Emphasis mine]

Therefore, since forcecage only describes the creature physically being inside the cage, and space does not represent physical size, a creature is trapped by forcecage if its body is fully within the cage, regardless of whether some of its space is outside.

To take your example (comment), a Storm Giant (MM pg. 153) is 26 ft. tall. It therefore cannot fit into a forcecage and therefore cannot be (fully) affected by the spell, regardless of whether or not its space is fully inside the cage. If the giant were to sit, or bend over, so as to reduce its height to under 20 ft., then it could fit inside, and could be trapped.

Physical size is everything, not controlled space.

Dragons

For this part of the answer, I am assuming that the measurements in the 3.5e Draconomicon apply to 5e.

The colour of the dragon is irrelevant in determining its size. The Draconomicon provides only a table of actual sizes by given size (tiny, small, medium, &c.). Although the table itself is huge (pg. 37), giving values for neck length, tail length, minimum wingspan, &c., I provide some of the more important values:

\begin{array}{c|ccc} \text{Size} & \text{Body length} & \text{Body width} & \text{Standing height} \\ \hline \text{Large (Young)} & 9ft & 5ft & 7ft \\ \text{Huge (Adult)} & 16ft & 8ft & 12ft \\ \text{Gargantuan (Ancient)} & 24ft & 10ft & 16ft \end{array}

Note that all of the values here represent not the maximum possible dimensions (i.e. tail and head completely stretched out), but the likely dimensions during combat (i.e. tail and head in).

Thus we can see that only the gargantuan ancient dragons are unable to fit inside a forcecage. However, dragons are clever creatures, and may stretch themselves out if they recognise that forcecage is being cast on them.