Frankly, there is not much you can do about Blender, it is in a deplorable state. Both .dae and .obj have broken handling of texture transparency.
For .dae, texture transparency has been completely broken since 2.8 released in 2019. It is ignored both in import and export, ie. everything is treated as if were opaque, like your third screenshot. I actually tried to send a patch for this last year but gave up after a few months.
For .obj/.mtl, Blender exports transparency from the alpha channel incorrectly (the way it exports is correct for a black&white texture being used for transparency, not for the alpha channel of an image being used). Obviously this means it would import wrong, so they broke the importer to import incorrectly too.
Neither .dae nor .obj/.mtl have a way to specify the blend method or backface culling, so there's nothing you can do about that. The .obj importer will always use alpha blend if there is transparency. There's a task about this on Blender's tracker. Maybe they'll switch to hashed or something one day.
As for two textures getting created when importing .obj, that's another bug in Blender (it's because of the color space), but a relatively harmless one, all things considered.
Can't tell you anything about .fbx.
For .dae, texture transparency has been completely broken since 2.8 released in 2019. It is ignored both in import and export, ie. everything is treated as if were opaque, like your third screenshot. I actually tried to send a patch for this last year but gave up after a few months.
For .obj/.mtl, Blender exports transparency from the alpha channel incorrectly (the way it exports is correct for a black&white texture being used for transparency, not for the alpha channel of an image being used). Obviously this means it would import wrong, so they broke the importer to import incorrectly too.
Neither .dae nor .obj/.mtl have a way to specify the blend method or backface culling, so there's nothing you can do about that. The .obj importer will always use alpha blend if there is transparency. There's a task about this on Blender's tracker. Maybe they'll switch to hashed or something one day.
As for two textures getting created when importing .obj, that's another bug in Blender (it's because of the color space), but a relatively harmless one, all things considered.
Can't tell you anything about .fbx.