You can create any formula that Excel can handle with XlsxWriter. To ensure that the formula fits the US version of Excel, you must be cautious with the formatting (which is the default format that formulas are stored in).
Therefore, if you use a comma instead of a pipe, your formulas should function as expected:
=VLOOKUP(B3,"Settlement Info"!$B$2:$R$2199,17,FALSE)
=SUMIFS("Payment and Fees"!$I$2:$I$6445,"Payment and Fees"!$B$2:$B$6445,Summary!$B3)
=IF(AND(I3>0,I3-N3>=-0.1|I3-N3<=0.1),"Yes","No")
This one should work without modification:
=+E3-F3-G3-I3
See this section of the XlsxWriter docs on Working with Formulas.