You can obtain the Smartsheet ID from within the Smartsheet you embed into Procore.
https://app.smartsheet.com/b/publish?EQBCT=88f2159870e34c33b9b0e3d068cc0e73
(The highlighted part is the ID you need.)
The Smartsheet you embed in Procore uses the same access rights as were set at the time of publishing, either read only or full edit. See this Smartsheet help article covering the differences between these options.