The home has an extremely comprehensive warranty for the first two years and I had the crazy thought of just not saving for any other expenditures for the first two years in order to save the cash flow from the home and money from my 9-5 to buy another home.

Legally, I can only increase rents by 1.8% under new ownership unless there is a capital expenditure or significant increase in property taxes that justify it. 

Given all the info and suspecting the owner is distressed by the expenditures, is $50k too low to offer for a 30 day closing with inspection contingency?

., replacing parts to maintain value.There is *cap ex* (capital expenditures) to make improvements. 

Vacancy and Capex are not cash out expenses, they are reserves that you should hold for when you do have vacancy or a large capital expenditure - so you have funds to pay for those items - and they will be expensed or capitalized in the year/month they occur.  

I don't think I'll cash flow here, so I ran my numbers only on the money I needed to pull out to have no cash in.Financed amount is $100,000The monthly mortgage payment came out to be $435.59 per monthAt a 5.125% rate on a 30 year loan, I calculated a Net Renal Income came out to be $1,140 per monthI split the difference of the range and used $1,200 for an estimated monthly rent and added in a 5% vacancy rate.Expenditures came out to be $613.73 per monthI used an 11% property management fee, which was $125.40.I used $120 for capital expenditure reservesI used $60 per month for maintenance reservesProperty taxes were $225 per monthInsurance was $83.33 per monthThis put me at a Net Operating Income of $526.27 ($1,140 rent - $613.73 expenditures). 

On larger properties, outside of performance calls, owner's usually get involved if there is a big bust in the budget (to alter the business plan if needed), capital expenditures are going to be more than estimated (find ways to cut costs if possible), or leasing strategies need to be adjusted to keep up with other competitive properties (example: providing concessions on new leases or renewals). 

Since I have been putting 100% into reserves, I don't know any different as to how much I should actually keep to be safe.My guess is it depends on the condition of the property and how much you believe will be coming up in capital expenditures. 

Am I correct that Capex is not counted in the operating expenditure, and as such is not reflected in the NOI? 

That factors in no budgeting for capital expenditures.