Hi David,
1. Is there a way to use the same custom field in several groups?
Yes, you can use the same custom fields in many groups (field ID, field type, other settings ...) but one field group has to be registered in one CPT only. Because if the page has two fields with the same ID, only one will be saved value to the database.
2. Can a field group be used in more than one custom post type (CPT)?
Like #1, it is possible. If you use the builder to create the field group, you can select multiple post types in the Location option.
https://docs.metabox.io/extensions/meta-box-builder/#field-group-settings
With the code, the meta box settings should be
'post_types' => ['post', 'my-cpt', 'page']
https://docs.metabox.io/creating-fields-with-code/