Unfortunately I don't have any bagatelle table plans for this type of table, and thus, can't give you actual measurements or formulas.
But, I did find a few tidbits to get you started or at least pointed in the right direction. One thing I can say for sure is that when I was searching for you, I noticed almost no standardization e.g. different hole sizes, different width between holes and the edges of the playing surface, etc.
This first one has a few measurements which, depending on your math skills should let you compute/derive some of the points you are looking for.
Next one may also help you decide on proportions and hole placement distance from edges. From an old patent image:
I also saw an old book that said the board's length and width proportion is:
between 6 to 10 ft. long, and in width about one-fourth of its length
And from that same book, another few photos which might help you measure out porportions and then scale them up to real-life size: