"This is regalia of Swedish Freemasonry. It is often on display in the museum. The Swedish system is comprised of 11 degrees. The first lodge was established in 1735. It works according to the Swedish Rite and allow male members that must be Christian. In contrast to the working of the majority in international Freemasonry it excludes believers in a supreme being who are non-Christians. However, a foreign freemason from a recognized obedience of any religion may attend lodges working in the degrees 1 to 6. Foreign visitors to lodges working in degrees 7 and higher must sign a statement assuring that they are Christian." I thought the image was cool. See http://www.mof.org.au/articles/items-of-interest/57-swedish-regalia.html
The statment regarding the VII degree is not correct in Sweden. We dont wear a top hat in Sweden from III but in other countries they do. https://grailquest.files.wordpress.com/2008/10/dsc_0006.jpg https://grailquest.files.wordpress.com/2008/10/dsc_0003.jpg https://grailquest.files.wordpress.com/2008/10/dsc_0002.jpg (The XI is R&K)
That is not always the case, and it's changing these years. I know that the Grand Lodge of Denmark have started allowing any brother who holds the necessary corresponding degree the right to visit in the degree from VII and above. Regardless of religious affiliation. However as usual, I'd suggest to reach out to the specific lodge in question before any visit, to check what they are doing.
So does Swedish rite start again from lev 1 and not continue after blue lodges lev 3 (thus lev 4 being first Swedish rank)
No the Swedish rite starts at 1°. All of the degrees where rewriten late 1700s to early 1800s by Charles XIII and a few select others to make a complete system. This is the reason for the christian requerment from the first degree.
The unique (and very cool thing) about the Swedish Rite degrees is that they are made as a continuous journey, so they are very much made in such a way that where the last one ends, the next will more or less begin. So you get a feeling of a much more complete system than I've seen in any other Rite. And Swedish Rite is also a blue lodge, system even though that doesn't really make sense to say, as we often consider blue lodge being 1-3rd degree. Best way of looking at it would be that it's a complete 10-11 degree system that starts as 1.
I know of one regular GL in Chile which is "Ancient and Accepted Scottish Rite" which which awards the first three degrees under the SR Grand Lodge.