As to spindle length. I've had three different very good bike shops swap out bottom brackets on three older bikes because I can never get the fixed cups out. In each case, they used a spindle length that was too short, because very few mechanics, especially those under the age of 40, know that older spindles were not always symmetrical. The drive side was longer. Too compensate, you need a new symmetrical spindle that is usually 3-5 mm longer.

In a couple instances the bike shops insisted they had used the longest length available. It was never true. They used the longest they had at that moment.

Sheldon Brown has a great page that tells you how to figure out what spindle length you need. Ideally, your center chainring or the center of your two chainrings should line up with the center cog of your freewheel. But being off by a mm or 2 isn't a huge deal.