Looking on the internet deeply has found these results:

Hope everything is going well is the most popular phrase on the web.

Hope everithing is well 11 results on the web	Hope everything is going well 113,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
Photographer. stevennnnnnnnnnn how are you??? where are you?? hope everithing is well...super super well for you. I'm in milan now i moved here !!! gabriel.	facilities and we hope everything is going well and according to [...] your expectations. viennafair.at. viennafair.at. wir heißen Sie bei uns im Hause herzlich. facilities and we hope everything is going well and according to [...] your expectations. viennafair.at. viennafair.at. wir heißen Sie bei uns im Hause herzlich. So, is "All is well" or "I hope everything is going well" incorrect? Should it be "I hope everything is going good" or "All is good" since it appears ... Feb 20, 2010 ... ... (by email) after several days' interval, is it proper and natural to start an email with "Dear xxx, Hope everything is going well with you."?

Hope everithing is well

11 results on the web

Hope everything is going well

113,000 results on the web

More popular!

Photographer. stevennnnnnnnnnn how are you??? where are you?? hope everithing is well...super super well for you. I'm in milan now i moved here !!! gabriel.

facilities and we hope everything is going well and according to [...] your expectations. viennafair.at. viennafair.at. wir heißen Sie bei uns im Hause herzlich.
facilities and we hope everything is going well and according to [...] your expectations. viennafair.at. viennafair.at. wir heißen Sie bei uns im Hause herzlich.
So, is "All is well" or "I hope everything is going well" incorrect? Should it be "I hope everything is going good" or "All is good" since it appears ...
Feb 20, 2010 ... ... (by email) after several days' interval, is it proper and natural to start an email with "Dear xxx, Hope everything is going well with you."?