For Solo ensemble we are required to number the measures of our solo (New Orleans -Eugene Bozza) but I have no clue on how to go about doing this.

Use the time signatures and figure out what notes go to each measure.

Cadenzas are usually pretty unstructured in tempo, but marking out measures may help in your interpretation. The cadenza should be more than just a bunch of notes; and never fast when they are quarters and slow when they are sixteenths.

No, don't go according to the meter. Most likely the notes won't add up to an integer number of measures. Count each bar thar is fully contained by barlines (for example note that the end of the third system has no barline, so the music since the last barline belongs to the same measure as the fourth system).

So the first system has two measures, the second system has one or two depending on whether you want to count the dashed barline, the third has two plus the beginning of the next, which continues to comprise the whole fourth system, etc.