To play it I go 1,2,3,4,5 repetition sign 2,3 use 2nd ending so 6,7. But at this point there is another repetition sign (the one at the end of the sequence) and I don't understand if it marks the end of the current repetition that I just did, or I have to repeat the whole sequence again. And if I have to repeat it again, would I go 1,2,3,4,5,2,3,6,7 again? So the whole song is 1,2,3,4,5,2,3,6,7 played twice?
Hello and welcome to Music: Practice & Theory StackExchange.
Traditionally, the last repeat sign, as a "right hand" repeat, would indicate that you go back to the left hand repeat sign at the beginning of measure 2.
So, measures in order, 1, 2, 3, 4, 5, (repeat) 2, 3, 6, 7, (repeat) 2, 3, 4, 5, (repeat) 2, 3, 6, 7 ... and you're done.
I would mention that in some traditions, first endings are skipped the second time through; this is typically for the sake of brevity, so it would not apply to a short example like this, and endings are not skipped in very formal settings either. One tradition where this is standard practice in the March tradition in wind bands (I'm from the USA, not sure about England, etc.), particularly in march music after about 1920.
It is unclear what it means, which means that whoever wrote it better include a note on what to do.
It could be a typo. In the Finale music notation program there are options for 1st and 2nd endings. When you click on the second ending option, the program automatically puts a repetition sign at the end of the second ending unles you untick "Create backward repeat bar".
I have sometimes forgotten to untick that and then I have wondered why there is a repetition sign in my second ending. It is frustrating until you realize what is going on.
Whether that is what happened in your case I of course don't know, but it is a good qualified guess.
PS.: I just saw @Kevin_Kinsey's replay regarding the different traditions. That is interesting, but it underlines that it is not clear what it means unless you know which tradition is applied with that particular piece of music.