Bagatelle? Trou Madame? Anyone up for a game!

Hi all, Just wondering if there’s any knowledgeable bagatelle players here on the dope? I’d never heard of until recently, but then on a random late night absentee bid, I bought myself a table from a local auction house! I’ve got a gist of the rules, but also have several questions about what I got!..

I was expecting a cue, but it seems this came with something called a mace? looks more like a one wood for pool, but do I just use it like a cue?, works well for getting the balls out of the cups, like a croupier with a rake might do?

This piece of timber that came with the game, slots onto these metal tabs halfway along the game surface, I can’t yet find any reference as to why, or for which mini game maybe?

Also curious about the age, and timbers involved in this piece, and although I left my details to be passed on to the vendor, I haven’t yet learned any history.

Thanks, should be some fun once I work it all out, welcome to drop in for a game sometime!