"Dinner" refers to the main meal of the day, regardless of the hour it is eaten, while "supper" is the evening meal, and may be quite a light meal.
I don't know how the Greek words are used by native speakers, but βραδινό is obviously derived from βράδυ, so left to my own speculation I would guess that it means "supper".
There is the word "μέρα" in the word "σήμερα". This happens in sooo many languages like Dutch (vanDAAG, though it's actually "dag" with one a), English (toDAY), French (auJOURd'hui), Latin (hoDIE, though it's actually "dies"), Russian (сегоДНЯ, though this is the genitive form, nominative is "день"). In Spanish (hoy), Italian (oggi) and German (heute) it's not visible any more, because the words have changed a lot in these languages.
That is not accurate. English allows adverbs in several different positions, but they cannot be inserted anywhere. One place where an adverb cannot be inserted is between the verb and its complement, in this case between the verb "have" and its direct object "fish".
I believe in the vast majority of cases, a native English speaker would put the adverb "today" either at the very beginning or at the very end. Examples:
Today we have fish for dinner.
We have fish for dinner today.
English uses very strict word order. What you wrote is not correct.
This is just an example of adverbs of time:
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