Alcohol strength is determined from the opening specific gravity (SG) minus the finished (SG). Usually determine SG using hydrometer.
How long it will keep depends on a number of factors; strength of beer, temperature and how much you draw off each day etc. The budget barrel you are talking about will have some co2 initially as you will carry out a secondary ferment in the barrel by adding sugar to the finished beer when you barrel it. As you draw off beer the pressure drops as the volume of liquid decreases. Usually the first few pints are very gassy, then it settles down and eventually not enough pressure to dispense beer. At this stage air can enter back via the tap and the remaining beer oxidises very quickly. Keeping the beer cool helps but unlikely that the beer will remain in good condition for long -couple of weeks tops? Look at a home brew site like Jims Homebrew forum lots of advice and tips there.
http://www.jimsbeerkit.co.uk/index.htm