I'm going to answer your second question first. The Amish resistance to technology is an outgrowth of their theology. Specifically, Amish people consider the outside world to be sinful, and put a high priority on maintaining their religion and community in as close to an unchanging state as possible. Keep in mind that Amish are devout pacifists. So when I say they think the outside world is sinful, I'm not really talking about booze and strippers, I'm talking about the existence of armies, countries and police forces.

What this means for technology is that the Amish take a very sceptical approach to any technology because it could either A) Change how the community works or B) further connect the Amish to the outside world. They don't have any objection to technological advancement as such. For example, it is forbidden for an Amish house to be connected to the electrical grid, because that would eventually lead to them being to reliant on the government that provided the electricity. But if someone broke their spine and couldn't walk, it would be perfectly legitimate for them to buy an electric wheelchair, and charge that with a gas generator they keep on their property.

Likewise, Amish aren't allowed to own personal phones. That would do too much to change how members of the community interact with each other. But most Amish communities will have a functioning phone somewhere that can be used in case of emergency.

So to answer your first question, the Amish didn't pick a time period to stay in with regards to technology. What they want is to keep their community and religion as unchanged from their founding (roughly the early 18th century) as possible. Technology is evaluated as to whether it can help (rarely) or hinder (almost always) that.