Start by importing the svg and entering edit mode. Then, select two handles on opposite sides of the center and press ⇧ ShiftS for the snapping pie menu. Drag the cursor down before releasing the keys to choose Cursor to Selected.
In object mode, press W or RMB for the Object Context Menu and find Origin to 3D Cursor.
With the origin now correctly positioned, ⎇ AltG will center the object in the scene.
Now convert the curve into a mesh via Object Context Menu > Convert to Mesh
To clean up the mesh, delete all but one quadrant since it is symmetrical across two axes. I like to quickly press X followed by V (the underlined letter in the menu) to quickly delete vertices or edges, faces etc. by using their corresponding underlined letters.
The mesh has a ton of extra verts on this corner. Let's clean those up.
Zoom in, select the unnecessary vertices and press ⎈ CtrlX to dissolve them.
Also delete every other vertex in the denser area on the right. Select > Checker Deselect can speed this part up significantly.
Now that the vertices are nicely distributed, the mesh can be symmetrized via Mesh > Symmetrize. Use the Direction settings +X to -X and -Y to +Y in either order.
Your mesh should now look like this:
Press F to fill the interior of the shape then press I to inset the face, creating faces around the edge. Delete the large face to be left with just the outer face loop.
Extrude this loop upward to the desired height with E.
The shape can now easily be deformed across any surface by parenting it to a Grid mesh (Add > Mesh > Grid), adding a Surface Deform modifier with the grid as the target, and shrink-wrapping the grid to a cylinder, for example.