Is it alright to use the same figure twice (but different figure number) in a report? If so, do I have to use separate captions, to avoid confusion in the table of figures?
Unless the figure is central to both problems discussed and quite a bit away in text from both, avoid this.
If the figure is, say, 2-4 pages back (not forward. Introduce it with first reference, then backreference. Don't make forward references) just reference it by name, "Figure X from page Y", don't copy.
If the second occurrence is chapters away but just a mention, with the figure being helpful but not essential, backreference it just the same.
If the FIRST occurrence is just a mention, and the figure is central to the second occurrence, this is where you are allowed to make a forward reference and place the picture by the second occurrence, mentioning it will appear and receive more detailed attention further on.
If the occurrences are chapters away, but still the picture is essential to both:
Still, it is plain better to have the other figure differ - if only in emphasis. Underline other elements, emphasize descriptions, crop - if it's to illustrate a different thing, it can illustrate it differently, mention the changed emphasis in description, and have the two be two different pictures.