As far as I know there is very limited  scientific research on the subject and what applies to some birds will not apply to others, no single character can be attributed to to one specific genetic control because in some cases many factors could be responsible, the melanization process is a complex process in which many factor come into play, so we also have to rely on observation and the experience of  breeders. Only when the canary genome is mapped will we get precise and reliable answers.

Canary color patterns are controlled by many pairs of genes, each pair or pairs of genes affects a different body area.
Two ticked birds (lipochrome with a dark marking) may never give you a ticked chick if they are found in different body areas, the same applies for foul birds (melanin birds with clear feathers).

A fertilized egg receives half of the genetic material from the father and the other half from the mother,during meiosis the genetic material recombines to form the new embryo, this recombination is different with every and each of the produced eggs, at this time, it's like pulling the lever on a slot machine you may or may not get the right combination for particular markings.

1. To answer your first question, it is not often that that a solid melanin canary develops clear feathers after the first molt and different bird lines or families will react differently. There are also cases where a bird continues to get more clear feathers with each molt and eventually the bird gradually turns clear from the head down,I have never seen them turn yellow, only white, this indicates that it might be a pigmentation disorder of the melanization process, another throwback is the halfsiders, these birds are  lipochrome on one side of their bodies and melanin on the other half.

2. As you can see your second question will be a matter of the recombination factor and the dominance and amount of genes implicated, if the right combination has been inherited the change will be visible, on the other hand it just may be inherited and carried.

3. When you breed a foul to a solid (self), the solid might break the inheritance pattern partially or completely but there is no guarantee, breed two foul an the chances of getting foul are highest, breed foul to self and you reduce the chances, logically.There is a tendency for the appearance of light feathers or light patches in all domesticated birds due to the inbreeding factor it has even happened in the wild.

Are you apt to get variegated offspring if you breed 2 birds with foul feathers together?

Take for example Gloster canaries, most have foul wings and tail and some variegation pattern, when bred to each other they tend to produce all chicks similar in pattern but once in a while you may get a mostly lipochrome bird or a self, it's just a matter of the slot machine effect.The variegation factor seemss to be of incomplete dominance this makes it more impredictable and random.

In the old days there were sections for competing evenly marked birds, yellow or white birds with two dark wings and a cap or dark tail or a saddle or any combination of these. The breeders accomplished this by pairing together similarly marked birds, over time the pattern could be partially fixed but not completely, Do not confuse this with  the London Fancy which was a mutation that always produced birds with dark wings and tail and was lost in the 1850 s.

In other words I don't have the definite answers to your questions, but I hope this helps.

ammed