Question about droplet "Region"

Dear DO community,

I did not yet create our first droplet, and my knowledge is moderate, so please bear with me. We want to setup a hosting environment to host a small PHP website-application for several client websites. These clients are located all over the world, so essentially it is a challenge to select the droplet “Region” … I am in fact wondering what the “region” selection involves …

1) Does it mean the server is entirely run from the specified “region”, handling ALL requests, processing ALL scripts, and serving ALL assets from the same location regardless of the location the request was made from?

I ask because “cloud” in other services offer refers to serving resources from multiple locations, thus to serve data closer to where the request was made from.

2) If the above is correct, is there any method to set an “origin” region, but then host the application across multiple regions depending on request? If so, are there additional costs involved? … would we have to create multiple droplets for several locations, and then have them “synch” or something?

3) For a main base “region” for global access, I wonder what the best choice would be … I am guessing east coast US, as that would be best compromise for US/Europe where most visits would be made from.

Excuse my lack of understanding and choice of terms, but hopefully someone with knowledge understands what i am asking! PS! don’t worry, I will have someone more able than me setting up the server, but I still want to understand how it works.