We want to create an Archimedes spiral curve 155mm long. The dialog to create Archimedes curves has three relevant parameters: (number of) Turns, Radius Growth, and Radius. This problem is under constrained, meaning there are an infinite number of values for these three parameters that will give us the spiral. We will need to pick two, then calculate the ...
Yes ! you need to use shrinkwrap method of curse
You need to join you dividing plane to your mesh :
then you need to project your surface with desire amount of resolution and apply everything
then you can select flat (extra faces) by select > linked > linked flat faces and remove remaining dividing faces .
and choose open edges by double click ( or ...
Like moonboots said, you can use vertex groups and weight painting to change the thickness:
Add a vertex group (Select your object, go to the green upside down triangle next to the materials tab and click on the plus icon)
Select the modifier properties tab (the wrench near the yellow square) and add the solidify modifier from the add modifier dropdown