Questions regarding indexes

Hello,

are these statements true:

• «You should always index fks. The only exception is when the matching unique or primary key is never updated or deleted» ?
• «Small tables do not require indexes» ?
• «Create an index if you frequently want to retrieve less than about ~15% of the rows in a large table»
• «Index only columns with unique values, or only with a few duplicates»
  

Is it necessary to run ANALYZE on the table after any index creation to gather statistics about the index/column?

Thanks
Bruno Lavoie