I am recently tracking my monthly expenses using the NAV on the DBS app. Should I exclude my monthly investment (excluding fees imposed) in order to have a better picture of what I am expending on?

I use DBS NAV too. I label my investment transactions (i.e. whatever $$ including fees that exit my bank account) with the "Investments" category. From there, DBS can tell you how much you saved (excluding investments).

Investments should not be considered as your savings.