That looks like wood, might be custom?

I think you see bars (serving beers) with stools and no overhang. These are fine for a social setting where one person might be sitting with their back to the bar chatting to others in the room. If you intend to use the bar for food you need to face the island so will need the recommended leg room. Could you swap the 600 deep cabinets for 300mm deep? The cost of new carcasses might not be too bad. You should also talk to your kitchen fitter as he may be able to install them after the quartz.

Hi, do you have photos of the space? Is it a light or a dark room? I would personally choose a white or light grey quartz or something like Silestone. Maybe a marble vein in it, like Calacatta Gold. You need to get some samples to see the colours in situ. But if it is a very light filled room, you could also go for a darker granite or quartz.

You can get worktops made to any thickness, granite and quartz usually comes in 20 or 30mm thicknesses but it can be made to any thickness and with different edge profiles, the underneath is packed with mdf and all the edges are made thicker. You can also get laminate worktops made extra thick by a laminate fabricator [google for a local fabricator], they would get/make the base board [chipboard] to your thickness and then bond the laminate sheet to the tops and sides [square edged]. There's also concrete worktops which can be cast to any thickness, copper and stainless steel worktops can also be made to any thickness. Also real wooden worktops can be made to look thicker by a decent kitchen fitter or carpenter.