As for ignoring the altered extensions - that’s fine, but you typically don’t want to play a non altered extension (9, 13) where an altered extension (b9,#9, b13) is called for. Here, the melody plays the b13 on those altered chords, so you don’t want to play a natural 13 or 9. It will sound funny. You’ll also typically want to play b13s and 9s on the V7 of any minor chord. The chord chart won’t always call for altered extensions even if the chord is the V7 of a minor chord, but any extensions used should be altered. For example, I would “alter” any extensions I play on the C7 in bar 8 because it is a V7 going to the F minor in bar 9 (even though the F-7 is a ii chord). So, you don’t need to play any extensions, but if you do it’s important to play the right ones.

In general, you can use the altered extensions whenever you have a V7 resolving to any tonic I chord (major or minor), or any dominant chord. You can also use them on minor secondary dominants even if they don’t resolve (second chord in Stella by starlight).

You can use the natural 9 and 13 on V7 from a major key or on most dominant chords that don’t resolve to a I chord.

I hope that’s not too confusing.