I do not understand the criteria for using ein, eine, einen. can anyone help me?
Well, you can take a look at "Notes and Tips" of the past lessons and this one. Then you will understand when to use a definite/indefinite article, depending on the gender of the noun and also it's function on the sentence.
Ich esse einen Apfel. - I eat an apple. (am eating) Apfel is masculine and also in this case, the apple suffer the action of the subject I, so it's considered accusative. Since you know that, you just have to check what's the masculine indefinite article for accusative situations.
It may sound a little bit confusing here, but if you check the Duolingo explanations and see the comments of others people, you would be better understanding this situations.
Hope it helps.
A desk is a table, but not all tables are desks. According to my dictionary der Schreibtisch = 'the desk'.
It's because the word "Tisch" (table) is a masculine noun. In German, different versions of "ein" (a) are used based on the case and the gender of the noun (this is one of the reasons it is so important to memorize a noun's gender as well as its name when you're practicing vocabulary). In this particular example, "Tisch" (a male noun) is being used as a direct object (accusative case), so the version of "ein" that goes with it gets an -en ending. Only female nouns use "eine" (and then only when they are the subject or direct object).
These are exactly the points Duolingo should be explaining as the lessons progress, but, for right now at least, they say little or nothing about German grammar. However, they've promised that will change sometime in the future. For now, look to other sites for more information on German grammar as you work through the lessons. Here's a link that shows a table of the various versions of indefinite article "ein" and when you use them based on gender and case...
Also see http://german.about.com/ for a lot of information on all aspects of German grammar.