The piece in question is 'Polish Song' by Hiller. I have labelled the bars from 1 to 11.
The piece is in A minor, and we seem to have A minor leading to V7 in the opening measures (I'm putting the C in the melody down as V13).
Bar 3: We have a G natural in the bass. I was tempted to sharp it, but there doesn't seem to be space for the A natural resolution at the beginning of the next bar, so perhaps this is minor chord v?
Bars 5/6: We have C E G, with B in the bass, which could imply a major chord III? (not augmented.) I flirted with the idea of this being V7 (with an added 13), but the melody notes in the next bar seem to suggest this does not resolve to the i chord. Any ideas as to what is going on here harmonically speaking?
Bar 9: seems to be V7 but in second inversion. If I put a G sharp underneath the B (to change it to first inversion) the texture becomes cluttered. As far as I know, this actually shouldn't be a legitimate place for a second inversion chord, as it is on the strongest beat of the bar and is obviously not part of a cadencial 6 4. So what is happening here?