Hi,
I give it try:
The total price is spread out over the total period. The price is 34,42 per night (incl servicecosts) or 32,66 per night (excl servicecosts). This price mentioned here is rounded up (2 digits: .66), in the calculcation there can occur a small difference like the $.25
The total amount of nights is 186. The final payment says 5 nights, but this is not mentioned correct: if check-out is on 1 may, it is 4 nights. It also explains the low nightly (statistical) price mentioned there. It does not effect the total price.
Why you pay more in the first month is not clear to me, maybe the cleaning fee is included there ?
To me the invoice looks correct when it comes to total price and the payments. Long-term-stay payments starts allways on date of check-in (here: 27 okt) and next payment starts on same date of the month (here 27 nov, 27 dec, etc..). The nightly prices mentioned at each payment is only for statistics, it is simply a (rounded up) calculation of monthly price divided by amount of days.
Hope this helps,
Emiel