"have been reported to be" is tautology must be "have been reported homeless"

You usually don't use "after" with the present perfect tense. If you use "since" instead of "after", it does work.

Will this phrase corect if use the word "still" ? For example: Many people are reported ti be still homeless after the floods Or Many people have been reported to be still homeless this week. Thank you for answering )

In the second sentence you're using the present perfect, which is normally used to denote an action that occurred in the past but still continues in the present. For example, it would be right saying "Many people have been reported to be homeless this week" (and the week is not over yet) but since you're speaking about the floods I guess they're actually over when you're speaking.

‘Have been’ is present progressive tense, which is followed by the present participle of the verb (the verb form ending in -ing.) Where as ‘reported’ is past tense. Here is the correct sentence - “many people were reported as homeless after the floods.”