Are braces, buckteeth and thumbsucking related?

Sort of. Braces (orthodontics) are used to correct "buckteeth", or teeth that are forward/protruding...Thumbsucking is one (not the only) of the causes for buckteeth.
Can be. If thumb sucking happens for extended time into the permanant dentition (after about 5-6 years old) or if the thumb sucking is very forceful during growing periods it can deflect the anterior teeth and/or cause changes in the bone that narrows the palate. Both of which cause there to be a "bucktooth" appearance.
Yes. Although thumb sucking past age 4 is not the only reason for buck teeth and the eventual need for braces, it can be an important cause. Effect depends on duration and intensity. Try to discourage thumb habit w positive reinforcement. If child unwilling or unable to quit, may need professional help. And see orthodontist at age 7.
Pretty much. The thumb is an incredibly strong "orthodontic device" as it can cause deformation of the dental arch form and can push upper front teeth out, lowers back. The excessive protrusion of the upper front teeth is called buckteeth. Orthodontic treatment can correct this issue often using braces.