Best way to export catalogs so someone else can open/edit them?

Yes, specifically you would want to make sure when carrying out Export as Catalog that the option "include originals" is chosen. This duplicates a corresponding subfolder arrangement into the target storage alongside the newly created Catalog, populated with duplicates of all the needed files (and only those). Therefore if there were other photos originally taken but then culled / not imported, these would be excluded by this process.

You can select all of the images desired, checking the option to include selected images only, if these are only a subset within your current Catalog. I believe (may be wrong) only those Collections in which these images feature - and only the keywords that they use - would then arrive. For Smart Collections I suspect you may get copies made of all those, so there may be some cleanup of unwanted stuff to do before sending off the disk. Also initially the new Catalog will not have Library previews made so if you want your client to have an immediately responsive experience navigating the photos it may be worth the trouble  of setting this Catalog to work yourself, in generating those 'up front'.

Yes, but you need to verify that she uses the same version of Lightroom. Older versions cannot open a newer catalog, and your version cannot export in an older catalog format.