How to make S4S see my .blend mesh file

You can not simply work with your own .blend file as the basis for your clone.

In order to use your own meshes you will have to clone an EA object, export that mesh to .blend and then, in Blender, import your own mesh and rename it/change its cut number to match the EA object. Once done you delete be original mesh in Blender, save the file and import it in Studio.

There are many, many, tutorials about this in the tutorial section of this forum. I suggest you look them up because Orangemitten has done a great job of writing this up step-by-step with pictures.

Well if you want to create many things for sims, you should read lot of tutorials and study how to do so, but ill give you a fast info on how to do what you want.
if you create a mesh in blender that is a object (like a painting mesh) you need to do the following to import it to sims 4:
i will show you how to make it in 9 simple steps, but if you want to really do it right u should study more.

1>Open Sims 4 Studio.
2>Under objects mark "create 3D mesh", and click on the object,choose item looks and function about same as your item, click ok, it will create a .package file for you, give it a name.
3>Go to meshes tab, and click export, this will create a .blend file for you, open it in blender.
4>Import you .blend file into the .blend you just opened.
5>Click your mesh to choose it, and then shift+click the "ea mesh" the one you exported, then click CTRL+J to joing them.
6>Press TAB to go into edit mode, click B and choose all the vertexes of the ea mesh and delete them, click B choose all vertexes of you mesh and position it where the ea mesh was, save the file.
7>Go to Sims 4 Studio and now press the import button and import the .blend file you just made into lod 1 2 and 3.
8>Go to texture Tab import your texture.
9>Save the the file, move your .package file to mod folder of sims 4 and you done.