Home Loans with Banks require you to have 20% deposit plus costs (fees, stamp duty, legal fees) since the introduction of LMI you are generally able to borrow up to 95% of the purchase price so you would have 5% deposit plus costs. I have seen LMI approved by the provider up to 98% but these are rare.
LMI is something that you as the customer pays for as insurance to the bank in the event you default. So the bank carries the risk for up to 80% and the LMI carries the risk on the 80-95%.
Banks will generally take a purchase price as value but the valuation officer does take into account local knowledge and current market trends. Bank valuations are not necessarily market value but a security value that the Bank uses as an estimate of market value. They have to look at it as what they could realistically sell it for today if you were to default on a loan.
You can usually pay a fee and have a sworn valuation done by one of your Bank's preferred valuers (which is separate to the Bank's valuation officer) who will do an in depth valuation (inside and out) and the Bank will take this into consideration with value.
For those of you unsure of what you've paid and why that isn't a great reflection on your Bank and shouldn't happen as all documents should be explained and understood before they should have you sign them.