The outstanding mortgage with interest is $175,000.I have been considering offering 100-125k for the building, but without a tenant upstairs, this only increases my costs --- at least for the next four years.

I believe that you would still have to disclose it on an FHA application, they want to know all of your outstanding debts and monthly payment amounts.  

Any suggestions for plumbers that work on commercial/multifamily in Ventura County, California?

I would imagine I should also probably run a title search and make sure there are no outstanding liens on the properties.

The key is that 2 year work history that you'll need to establish.In certain circumstances you can use the income before you even receive your first paystub (certain relocation and job change scenarios), however typically you'll need to receive atleast 1 paystub to use it.If you have had no work within the last 12 months preceeding this new job then you may need to be on this job for a min of 6 months before you can close on this new loan which would hamper your plans to close within 45 days on this duplex.Then again scenario #3 if you have the credit and the down payment and the property cash flows from conventional underwriting perspective and you have "no credit card debts," on your credit report then you may be able to qualify any way since your debt to income or DTI will be 0% (property cash flows) no debt outstanding to qualify for as the duplex will be adding income to your scenario.I've had an underwriter okay scenario #3 above but have never funded a deal like.

How can I make sure if there is other lien or any other outstanding cost associated to the property?   

Sure, I got the title search part and a need to pay off whatever outstanding liens may be there.

Although I did not retain her because I do not have enough properties to justify PM expenses, I definitely feel her knowledge in PM and drive for results are outstanding.

@Jason Hirko @Dmitriy Fomichenko and @Mark Nolan, gentlemen thank you for the outstanding information.

Riley Hinshaw the biggest outstanding question is whether it is a deal.