Checking the normal form of the current table

The mistake is in your understanding of transitive dependency. From wikipedia: Transitive dependency

In mathematics, a transitive dependency is a functional dependency which holds by virtue of transitivity. A transitive dependency can occur only in a relation that has three or more attributes. Let A, B, and C designate three distinct attributes (or distinct collections of attributes) in the relation. Suppose all three of the following conditions hold:

1. A → B
2. It is not the case that B → A
3. B → C

Then the functional dependency A → C (which follows from 1 and 3 by the axiom of transitivity) is a transitive dependency.

In your case though, (2) does not hold:

1. U → T                                  -- correct
2. It is not the case that T → U          -- wrong
3. T → V                                  -- correct

Therefore {V} is NOT transitively dependent on {U}.

If all your dependencies are those you have shown: {A->GH, B->IJ, C->A, F->B, FC->DK, K->E} then you have come to the wrong conclusion.

Your only candidate key is CF. The C and F are not candidate keys on their own.

Therefore, the F->B dependency (and the C->A as well) means that the relation violates 2NF.

For the other question, if you had for example these dependencies:

BC -> AF
AF -> BC
 F -> DE

where the candidate keys are BC and AF, then again the F -> DE would mean that the relation violates 2NF. To be in 2NF would mean that there is no dependency on any part of any candidate key.