In this scenario it is very tricky depending on the end buyers finances if you are looking to sell it to an "end buyer" and not an investor. 2.

It depends on what exactly you are referring to with gap funding.

Depending on the market you invest in, you may have enough to go all cash on the first deal and refinance to put money in the second deal. 

depending on where you are in NJ you might have the Lehigh Valley in PA a couple hours away, or Delaware, etc. you can go to meetups, see places in person, and start to build a network.

(Usually you cannot use prior employer history until you have been at your new job for 6 to 12 months, depending on the underwriter to show that you are maintaining the same level of bonus/overtime/commission income that you had at your prior employer).

As far as timeframe, anywhere from 21-45 days depending on how quick a borrower gets their docs to underwriting, how long the appraisal takes, etc.

Quote from @Alex Clark: Looking to buy a property in Ohio Depends.

They have lots of options for you, depending on your budget.

Days on market are around 80 days on average, depending on the area.

From the numbers perspective it seems like it can pencil out depending on the rehab budget.