To articulate those notes I often use a ‘t’ sound. I teach this in step 9. You motion saying ‘T’ as you play the note. The other thing that helps is to have good control of the breath, to keep the notes steady in relation to air flow.
Angie Is in the key of C (or A relative minor), so your in luck as far as being able to use your C diatonic harmonica to play along with that recording. I’d suggest using the C major scale taught in lesson 2 and try improvising by following the melody of the vocal. Close your eyes, listen and play what comes to your heart.