What’s the difference between a reprint and a new edition?

A reprint means more copies are being printed with no substantial changes. Perhaps a few typos are being fixed. A new edition means that there has been substantial change: content has been altered in a way that might make a customer complain that this was not the product that was expected. Or, text has been changed to add a new feature, such as a preface or appendix or additional content. Or, content has been revised. Or, the book has been redesigned.

If a second edition has the same title as the first, does it keep the same ISBN?

No. A new edition is considered a different product and gets its own ISBN.

How are ISBNs assigned to multi-volume works?

ISBNs are assigned to the volumes as they are sold as products. If they are only available as a set, the set gets one ISBN. If each volume is available separately and as a set, each volume gets an ISBN and the set gets an ISBN.

From: ISBN.org

Are different ISBNs used if a book appears in different languages?

Yes. Each language version is a different product.

From: ISBN.org