How can I merge these two spherical objects into a single smooth mesh? I have two round objects as a part of my overall model. I will be exporting this model and using it in a game I am making.

Last time I did this, I had around 15 different objects in my model. I didn't like this for several reasons. One: I had to merge all the objects anyway before exporting, so there was no point to having separate objects. Two: I ran into issues when UV mapping where I couldn't tell what part was what because there were so many different complex objects. Three: I was worried that having invisible surfaces inside other surfaces might negatively affect the render performance of my game.

For all of the above reasons, I decided to try to remake my model as a single joined together mesh. This leads to my two questions:

Question 1
Is this even the right way of going about this? Should I be trying to create one connected mesh or should I just leave the model as a bunch of disconnected objects merged together? Why or why not?

Question 2
Assuming creating one smooth, merged model is the right way to go, how would i merge the two objects in the image below? I know how to join them, but not how to merge their vertices and delete their insides in such a way as to create a single, smooth, connected mesh.
To simple ways, to help keep track of the UV mesh:


In edit mode in the 3D view press Shift+L to select an island of linked vertices. Then hide all other parts with Shift+H. Only the previously selected connected vertices are shown in both 3D and image editor.
When trying to identify meshparts in the uv / image editor, this button may help. 


If your game engine is struggling, deleting additional vertices, which aren't shown anyways, can increase performance. (This also depends on the game engine.) Otherwise, leaving the mesh in whatever state is best maintainable. If joining them is the last step before exporting, I would suggest keeping your work blend file intact and doing mesh joining step separately.

If your performance is fine, hidden faces are no problem.

If you wanted to merge two spheres into a single object and remove the hidden vertices, do the following.


  
  Add a Boolean Modifier to one of the spheres.
  Set the other sphere under the Object in the Modifier Tab.
  Set the Operation to Union
  Apply the modifier.
  
  
  
  
  
  Delete the other sphere.
  


This will cause problem with smooth shading. (Triangles)



With spheres there is an easy fix. We can use the topological features of the spheres to get rid of topology problems. Do the following steps before the boolean operation.


  
  Select one of the spheres and add a Damped Track Modifier, with the other sphere as the Target.
  Do the same vice versa (with the other sphere).
  Set one of the Damped Track Contraints to To: Z and the other to To: -Z.
  
  
  
  
  
  Select both spheres and Apply Visual Transform (Ctrl+A > V). (Optional)
  
  
  
  
  
  You can now delete the constraints.
  
  
  Do the Boolean operation and delete the unused sphere as explained above.
  
  
  In edit mode, select all A then remove doubles W > R
  
  
  


Smooth shading now looks fine, add edge loops to sharpen the crease.



With different objects, you will have to use different approaches to get clean topology with boolean operations.