I'm not 100% certain I fully understand your question, but you may be able to purchase a foreclosed home for less than it's listed price. Time on market and whether or not it will relate directly to a lower list price to sales price ratio is going to be heavily dependent on the specific investor that owns the loan's criteria for that loan. So, this is not even bank specific. Most banks act as servicers (they collect payments on the loans). They have various investors they work for (Fannie Mae/Freddie Mac/Private Company ABC, etc.). Each investor is going to have specifics they will look for in various parts of their portfolio of non-performing debt (i.e. foreclosures). This information is rarely shared with anyone outside of the bank/investor relationship.
For your second question, I'm guessing you're asking if you can get a loan for more money than the purchase price of the house so you can use the extra money to fix it. The simple answer is yes. A more comprehensive answer is yes, but it may not work for you. The most common form of loan like this is called an FHA203K loan. Or "FHA Rehabilitation Loan." This type of loan will allow you to perform a limited amount of work to the property. If you may be inclined to consider this as an option you should speak with a mortgage originator who is well-versed in FHA203K business and has actually closed several.
My background is in lending. I sell real estate and I have also rehabbed several properties in the last year, so I'm relatively familiar with purchasing foreclosures and the process in it's entirety. You're welcome to call or email me any time with any further questions.
I hope this was helpful,
Licensed in IN and IL