Are there any "conventional" lenders that would allow this?

There have been a lot of opportunities and I would like to flip one on my own but having issues with conventional financing on flooded homes. 

I was pre-approved for 350k conventional or FHA.

Then hopefully after 3-6 months of getting it into shape Refinancing the house using a conventional loan at 80% loan to value, and paying back the entire 401k loan.

Rents for apartments/condos have actually started to decline recently with all the inventory that's come online over the last year.

Can I get a conventional mortgage with 10% down on a 3-unit building where one of the units is a commercial space accounting for half of the square footage?

Remember, inventory is at a premium and you are in control.

You might want to check pricing, inventory, and regulations here before you jump in.

Looking to explore options for owner occupant lenders outside the conventional limits that borrow in Chicago to high credit/income individuals with under 20% down.

It's always a good idea to know the basics of Property Management, however a lot of information is available on BP and other places, so if you're primarily looking to build your inventory of homes, it's wise to learn how to do deals and start making offers.