Are these expressions okay?
1. He will come here by the 7 o'clock train.
2. He will come here by 7 o'clock train.
3. He will come here on the 7 o'clock train.
You won't actually hear "he will come here" by any train, in any English dialect. We'd say arrive, or come.
Let me confirm one more thing.
"* went by the * o'clock train" is found in native speakers' writings.
Is this a non-standard expression or "went by the * o'clock train" is idiomatically exceptional?
1. I don't entirely agree with konungursvia when he says, "You won't actually hear "he will come here" by any train, in any English dialect. We'd say arrive, or come." It may not be common, but it's possible.
2. In your example (above), will come is now went. Still, with COME or GO, on is probably more common, but by is possible.
My point is that "come here" is a particular sort of phrase, and is usually imperative. If you're using a future indicative mood and tense, just "come" would suffice, and sound natural. Or, you could use "arrive". But in such a case, "come here" sounds like a non-native mixing registers.
I am suggesting it is not very natural when juxtaposed with a means of transport. Perhaps you're getting too used to Czech, and have lost touch with English to some extent.