In Elasticsearch all fields are indexed individually and at query time the indices of multiple fields will be used, not just a single one. In the example you mentioned both indices will be queried and the sets of matches will be combined based on the logic of the query. The restriction that only one index can be used, which exists in some databases, does not apply to Elasticsearch.
There is no need for this.
The shards return information about the matches they have identified to the node coordinating the query, which I believe is enough to score and sort. I believe only the documents that are to be returned are fetched from disk.
If I recall correctly (have not used this feature much), the sorted index feature is a very specialised feature that optimises data on disk if you have a specific sort order that you always use, and can cut latencies this way. The trade-off is that it adds overhead at indexing time and does not help for any other sort order. This is therefore something that you only typically use for very specific scenarios.
This is in no way required for search after functionality.
Sorting in different ways is standard and efficient in Elasticsearch and does not require any special handling. Just use a standard index.