Here according to me the left side time signature is 9/8 and the right side is 4/4. Am I going down the right path or are my thoughts wrong ?
Both correct. 9/8 needs to be 3 groups of 3 quavers, as shown slightly less complex in bass clef bar 2.
4/4 is written best when the bar can be split into two equal halves, each containing the equivalent of 2 crotchets. Last bar, treble clef shows two halves, each with just that - 8 quavers. Well done!