Can you explain why we might have KEY `nm` (nm) and FOREIGN KEY (`nm`) in further detail?

How can we decide when it's better to use indexes to make queries faster or if it's better to not use them for a faster insert/delete?

Could you explain B- and B+ trees again? I'm having a hard time finding the connection of those with the rest of the reading, or how to even implement a B-tree in the context of SQL

Could you explain a bit more of how B-trees work? I don't understand how increasing the base of the logarithm changes the complexity of accessing a record to O(1).