Whether or not a watch band will take an electro plate depends entirely on the band. If it is made of stainless steel, most jewelers do not have the capability to plate the band adequately. If they can do it at all, the plate would likely be quite thin and wear away quickly. Also, if the band has steel parts in it, electroplating solutions can be damaged. I believe it would be quite difficult to find a jeweler who would try doing the watch band.
There is a chance a jeweler can send the band out for plating, as well as the ring. This "farmed out work" will generally go to a plating company specializing in that work with the high level equipment and experience to do a good job and render a thick enough plate for better durability.
One company is Red Sky Plating. Jewelers can send items to this company for estimates and to get the work done properly.
To gold plate the ring would not be difficult for any jeweler with gold plating solutions. Keep in mind, the thickness of the plate and durability cannot be assured with most jewelry store plating services done in-house. For the best results, I would suggest the ring be sent to the company mentioned or to a similar company. You could have a jeweler gold plate the ring and then "try it" to see how well the yellow surface lasts.
Various items sold to "consumers" for coloring metals and adding a microscopic silver or gold color generally do not last long and are not effective overall, in my humble thought.
The "dipping" process is called "rhodium plating." Rhodium is a precious metal and plating is a less expensive alternative to platinum. (There is no white gold in nature.) The plated finish is long wearing and may not need to be redone for years depending on your wearing habits. If you were a client at my Zales location the plating would only be about $24.00.
One nice thing about rhodium plating is that it offers an option to people normally allergic to the nickel in lower-quality gold. The plating provides a barrier that allows many such people to wear 10k and 14k jewelry.
Normally in Hallmarking, the numbers represent the decimal for the gold quality.
For example 375 or .375 is equal to 375 parts gold out of 1000 or 9ct. If this were a genuine hallmark then 750 or .750 would be 750 parts gold out of 1000 which is 18ct.
777 does NOT fit any standard gold hallmark (being just over 18ct if it were) so I would suspect it may be a makers mark or design or model number.
