"Isn't the train late?"
Is this some kind of more informal way to say it, since the は particle is dropped after 電車？
Particles are very commonly dropped in spoken language. For exaple people may say "nihongo hanasemasu" instead of "nihongo wo/ga hanasemasu". It is not less formal, it's just a difference between written language and spoken language.
It is definitely less formal. You wouldn't address someone you don't know this way.
I have many Japanese friends, and when I am confused I often ask which way they would say it. The number of times I have heard them say, "I would choose any of them" or "That doesn't make sense" is huge. Remember how many languages are available and we are learning from an algorithm written by a programmer. Don't be to harsh. Try and seek your answers from a variety of sources, and make Japanese friends if you are lucky enough to. がんばってみんなさん。よくできてる。
In English, there is a slight difference between "Isn't the train late?" (Seeking affirmation about the train being late) and "The train isn't late?" (Surprise that the train isn't late when you expected it to be). What would be the difference between those two questions in Japanese?
Being late, is not the same as being slow ... 電車、おそくないですか？ OSOI means slow ... right? so What about 電車は遅れていませんか。 (Densha wa okurete imasen ka.)
I think the reason is that would be very casual and improper if talking to a stranger.
Apparently, the particle is often dropped in spoken Japanese, so it's an important thing to learn about.
Dou should teach the correct answers to this negative question, since it is very logical.
Is the train not late? Yes means the train is not late, which means it is early or on time. No means the train is not not late, which means the train is late.
I'm always thrown off when there's no particle, but then I think to myself "oh yeah, a pause/comma can be an unspoken particle for ideas."
Thar makes it into a statement as in 'the train is late' rather than a question, which is why 'か' is added. Although 'isnt it' should probably be 'ですね' as it seems the answer is translated more like 'is the train late?'
Also, it would be おそくなります to mean "to become late", since おそい is an い-adjective. For な-adjectives, add になります after the base form of the adjective to mean "to become [adjective]" (e.g. きれいになります).