Banking Paperwork
If it is a conforming or super-conforming loan then usually the most recent complete statement will do. "Complete" is the operative word. Your lender will want every single page of the statment including blank and boiler-plate pages. If the statement says "Page x of 8" then the...

Lender wants to pay the upfront LPMI to beat another lender that doesnt' require LPMI due to former lender's low appraisal?
If there is upfront PMI is there also annual PMI you would have to pay? Is this an FHA loan?A little more information would be helpful. What is the loan amount and what was the appraised value? Your address would be helpful too just to cross-check the appraised value.

Looking to purchase rental property and will live in one unit. How much down payment is needed?
The devil is in the details but with an FHA loan you can put down as little as 3.5%. A lot depends on the purchase price, credit score, etc.

Are there any no PMI lenders on 15% down jumbo?
There are lenders that offer Lender Paid Mortgage Insurance. There is no separate MI payment. Instead the interest rate is higher and the lender pays the mortgage insurance. The interest rate is higher than if you paid the MI yourself, but usually the monthly payment is lower overall. And there may be tax...