The exact timing of when the Swordsmith Village Arc begins in the manga is a bit tricky to pin down precisely. It could be different based on how it's distributed. Your best bet is to look for information on manga platforms or from fellow manga enthusiasts who are up-to-date on these things.
The Swordsmith Village Arc typically begins around a certain point in the manga series. However, the exact starting chapter can vary depending on different translations and editions. You could try looking up reviews or summaries to get a precise answer.
The start date of the Flash Wars story arc can vary depending on the publication and series. It's best to look up the specific comic series or check with dedicated comic fan communities for the precise start time.
It can vary a lot. Sometimes the arc starts right from the beginning when the main characters meet. Other times, it might kick in a bit later when there's a major conflict or turning point in their relationship.
The encounter could change the power balance in Alabasta. If they form an alliance, they would be a formidable force against any threats in the kingdom. This might lead to a quicker resolution of the internal problems in Alabasta.
I don't have the specific date for when the Egghead Arc started in manga off the top of my head. But you can probably find it by researching on manga-related blogs or by asking fellow manga enthusiasts.