The 2 vertical edges are ripped:
If I select a vertex, here is what it gives (so you can't join the 2 opposite vertices):
So you need to delete these 4 faces + one horizontal edge that is under the faces (as pointed out by Batfinger, probably the result of a fill (F):
Then select the top and bottom row of vertices and press CtrlF > Grid Fill:
Select few unwanted faces (one in each X, Y direction)
Search for Select Similar > Normal
Separate P by Selection and hide newly generated object
For faces oriented Z use type Co-Plannar because type Normal takes into acount too many top faces
you can delete them directly, but it is better to check if in this separation isnt a face you want to ...
You should to add more edge loops in blue side , Equal with red side to join , then add one loop between red and blue side and Bevel to have a curvy conection .
Upload Blend file to show you how it's possible .
Ok here we are, I've fixed all by improving the topology.
So basically I recalculated the number of edges for matching it with the faces on the surface
Then I erased the faces and made a bridge edge loop
Added and applied a warp modifier with sphere fallout
Added a loopcut to fix those nasty shades and joined this part with my rim and made a bridge edge loop ...
Have you tried to switch on the Auto Smooth option for Normals on the rims? It prevents artifacts that can occur when the Boolean modifier is used on curved surfaces. Depending on your geometry you have to adjust the angle value (default is 30d) or add a few more edge loops. (Looks like you have only 2 rings but many edges for the "walls" of the ...
Snapping works with Z+ orientation, so just flip the origin point upside down.
To keep the parented objects in place, you can choose to only affect the parent.
Select your object
Go View > Affect Only > Origins and Parents
Rotate the Origin by 180°
Since your mesh is just vertices and edges, the solidify modifier faithfully maintains the lack of faces. Therefore you will likely want to use 'Grid Fill' to fill in the shape with quads, or manually do so by selecting three connected edges on your loop and pressing 'f' to fill them in with a face (automatically creating the edge necessary to form a closed ...
To extend comment above by @Tomáš Hübelbauer with screenshots.
For latest version of Blender(2.80+), to display edge measurement you need check this checkbox:
If you want use cm permanently (as I am) you should go to "Scene Properties" tab and select Metric then length. See the picture below:
UPD: a bit later I came across this video, explaining ...
You have edges going across faces.
Remove the edges that go across these faces by selecting them, pressing x and selecting delete edges.
Next select the vertices that were left behind and press j key to join these vertices
The end result is quite good.
You should use Connect Vertex Path J, which split the existing face.
Instead of New Edge/Face from Vertices F, which created a new edge on top of the face.
You need to:
Unwrap again, your islands are probably overlapping, choose the Smart UV Project option with a bit of Island Margin (0.03).
Put a bit of bleeding in the N panel > Tool > Options so that the paint correctly covers the islands.
Your image is currently 1024 pixels large, depending on what kind of shots you want to do it might be a bit too ...
Actually it may be easier to do it directly in an image editor but what you can do is switch the Film to Transparent in the Render options:
Then choose the front orthographic view and in View > choose Viewport Render Image (or render an image with your camera in front and orthographic view). The generated image has an alpha transparent background: