1) The easiest is to re-use an existing stackup
If you need a new stackup, depends on a project, but it can easily take 2-3 weeks to communicate with PCB manufacturer. Normally, if we need a new stackup we ask for it when everything is connected and I know we still need at least 3 weeks completely finish the PCB. Otherwise, as @mairomaster mentioned, the best is to ask "once you have a good idea about how many layers you will need". (PS: We normally route PCBs with track width and clearance bigger than we are expecting to have them and make the tracks thinner by the end of the layout to meet impedance requirements. However, if you do not have final stackup before you start layout, differential pairs usually needs to be re-routed).
2) We always provide BOM to assembly house - together with the components they should fit.