I appreciate if you answer below my query;
Is the party still on for next Friday?
Regarding above sentence, why does this sentence need “for”? It seems that it is enough for that without “for”.

See a translation

I [would] appreciate [it] if you [could] answer my [query below];
I [will] appreciate [it] if you [can] answer my [question below];
/question is more casual, query is more formal!
The same with [will vs would], [can vs could]

For your question, they both have the same meaning, but just that the addition of "for" makes an emphasis on the subject behind it.

1: Is the party still on for next Friday?
Emphasis/Subject on "Next Friday", feels more like checking about that day.

If you're confused you can flip the sentence,
"Is the party still on for next Friday?" = "For next Friday, is the party still on?"

2: Is the party still on next Friday?
Emphasis/Subject on Party

There is a little nuance!