A 20% down payment is a guideline. Many borrowers can get a mortgage for less than 20% down, but this comes with PMI and the added risk of being upside down in the house if you need to sell it in the not to distant future. I have always put down 20% myself, so I am not 100% sure as to how the process works with getting rid of PMI. My understanding is that once you hit 20% equity you need to write a letter to your lender demonstrating you are a 20% equity in order to get it dropped, I'm not sure how painful of a process this is.
There isn't a program to waive closing costs that I am aware of, but there are some options for not having to come off the cash. The first option is reverse points. Borrowers often pay points, each point being 1% of the value of the loan, in order to buy a lower interest rate, essentially paying points is pre-paying interest. With reverse points, the bank pays you to take a higher interest rate. This can be beneficial if you need the cash now and most likely won't be carrying the mortgage for the full term. Reverse points can be issued only to the extent that they negate the closing costs. So if closing costs are $3,000 you can not receive more than $3,000 in reverse points.
Another option is to ask the seller to cover $X of closing costs.
There is the fannie mae homepath program for buying foreclosed houses. The program offers 5% down payments, no PMI and "expanded seller contributions", which I think means they would try to get the bank that owns the home to pay some or all of the closing costs. http://www.homepath.com/financing.html
As far as escrow goes I prefer to pay the lump sums myself. There are many reasons for this. First of all, if you pay in escrow, they hold a certain amount of months in reserve, and adjust your payments on what they think your bills will be. They often overcharge, leaving way too much money in escrow. Another reason to avoid escrow is to keep a closer eye on your taxes and insurance costs. Mistakes can be made on these bills and you might not catch them if you have escrow. You also get a discount on home owners insurance if you pay in full. The only reason to do escrow besides the bank not permitting you to forgo escrow, is if you are bad at managing money, and don't trust yourself to make the tax payments and insurance payments yourself.
When it comes to HOA fees it depends on what the HOA does. I personally think any amount is too much and under no circumstances would I live in an HOA. I don't want the restrictions of busy bodies telling me I can't have a basketball hoop in my driveway or paint my house a certain color, or have certain types of plants. I have also heard to many horror stories of HOAs foreclosing on peoples homes for a few hundred bucks and selling them.
Income, Credit, Debt ratio and down payment are all large factors in getting a loan. Any of those 4 categories can stop you from getting a loan, on the reverse side those factors can also lead the bank to want to lend you more house than you can truly afford.
Base the house you want to buy on your income. I like the Dave Ramsey rule of thumb of keeping the monthly house payment at 25% of your monthly net pay on a 15 year mortgage. For a median household earning $51,000 a year, lets say $45,000 after taxes, this would result in a house payment of $865 per month. The bank is willing to lend upwards of 40% of gross!
Having bad credit, especially outstanding debts that aren't being paid are a big red flag to lenders. Having large payments are also a big red flag. The banks have guidelines for how much your debt payments can be total as a percent of your monthly income.
Having a down payment is important to buying a house. They charge PMI for those putting down under 20% because it is a higher risk loan, they also charge a higher interest rate. I would highly recommend taking the time to save up a 20% down payment in addition to having a 6 month emergency fund.
As far as lenders go I have found that shopping around is necessary. The last time we looked for a home mortgage we had a $5,000 swing in closing costs. There were 2 local credit unions that we were members of that had a major difference in closing costs. There isn't a solid rule of thumb on this except to shop around and compare lenders.
I hope this information was helpful.