1.5 Cars are a major source of pollution in cities. There are lots of different sources in this World but this source is singled out and defined so it should have been 'the major source of pollution' instead.
What's wrong with my version?
There's nothing wrong with your version, it just means something slightly different. a major source means one source among other large sources that contribute to pollution. "The major source" pretty much means the single largest source.
1.6 'I want to show you a photo of Jane and me.' A photo is defined by the second part so we know what photo the speaker decided to show.
Which photo it is isn't defined well enough to use "the" in that sentence by itself. If you said that, it wouldn't sound finished, and the listener would need to ask which one. For ex: A: 'I want to show you the photo of Jane and me.' B: 'Which one?' A: 'The one I was telling you about where ...' In contrast, your original sentence stands alone and could be any photo of Jane and the speaker.
I might be wrong and the last two examples don't strict the number of possible photos/sources enough to choose THE.