As a native speaker, I have never regarded these expressions as having any connection with or being euphemisms for "My God". They sound rather old fashioned by today's standards but are "safe" expressions you can use with English speakers who will not be offended in any way. Unfortunately, and here I am perhaps showing my age, people in English speaking countries are tending to use much coarser language than was so thirty years ago.However, there is no need for you to succumb to this tendency so keep it polite like these expressions.

Its kind of like a polite way of saying oh my god without offending others by saying gods name, but allot of people do say oh my god or omg, for when they are shocked or surprised. Most people do not make much of a big deal about it, at least in California. Good luck

Yes. For example, the original lyrics to the Cole Porter song "Anything Goes" were "In olden days a glimpse of stocking Was looked as something shocking But now God knows-- Anything goes!" In the 1950s a wave of prudishness swept over the United States and the lyrics were changed to "In olden days a glimpse of stocking Was looked as something shocking Now Heaven knows-- Anything goes!" (E.g. Frank Sinatra's version, https://www.youtube.com/watch?v=wYahz6VIpIM 0:12) A modern rendering of the original version: https://www.youtube.com/watch?v=qW_sd4GYsR4, 1:00

Basically yes. Similar Euphemisms used in the USA are expressions like this: "Gol--Dang---It" "For the love of Mike!" "For Pete's Sake!" "Golly---Gee---Willikers" and many other such outdated and best forgotten expressions.

Yes, they are all euphemisms for 'God', and there are more : 'golly' is another one. Some of them are old-fashioned, and others are specific to certain regions: 'gee' , example, is only used in North America, as far as I know. These days, very few people are offended by the casual use of the word 'God'. In fact, it has almost lost all religious associations when used in conversation. There are many native speakers, particularly younger women, who say 'Oh my god' between every phrase they utter.