wow..lots of questions! You need to read a basic book on hybridizing...you need a goal, too..
First..when you cross 2 plants, no telling what you'll get..plant them out and cull the weak and plants that don't have what you're looking for.

2. No..they will not produce identical melons, but generally..may make your crosses stronger..but not stable..they are two different things.
   3. New hybrids
   4. read up on "inbreeding depression"
   Buy yourself a good book on hybridizing!!!!!

If you want things to be easier, you should have Congo be the mother and Sangria be the father. The reason is that Sangria is already an F1 hybrid, and isn't stable. So, you'll be able to tell if Congo is a cross more easily, since it'll just be Congo (and look/taste like Congo) if it didn't cross. Whereas, if you have Sangria F1 as the mother, it'll still be different whether or not it was cross-pollinated. You could easily breed new kinds of watermelon out of Sangria without doing any crossing.

If you're confident you can do the cross, I'd say, do both. That way you can see the differences the different kinds of DNA have on them (e.g. mtDNA, cpDNA, etc.) I believe the mother line normally passes those down (sans the regular chromosomal DNA, half of which comes from each parent).

The first generation of your crosses will have all of Congo's dominant traits. Because Sangria F1 is an F1 hybrid, its dominant traits might be heterozygous, which means they might not pass onto the children; those that aren't heterozygous will be passed on for sure to the first generation of your cross.

The second, third, etc. generation of your cross will be much more varied in the results. To stabilize the cross, you'll need to make sure each gene is homozygous. All expressed recessive traits are already homozygous. It's the expressed dominant traits you need to worry about, because they can have hidden recessive alleles.

Of course, genetics are probably a lot more complex than this—but it's a start.

Breeding entirely new watermelons through hybridization is going to be a lot easier than trying to stabilize the F1 hybrid (and you might find it more rewarding)—because then you don't have to worry so much about getting a specific set of traits. As long as it's stabilized and you like it, you're good to go.