- In the sentence, escribo is the verb. Escribir turned to Escribo, because of the subject Yo.
- Propio is the adjective, must match the noun carta.
- Carta is a feminime noun (la carta = article la- infront of noun indicating carta is feminime), so propio changed to propia.
- Since the noun cartas in the sentence is plural, then, propia became propias.
Here's a link that is a good introduction. You'll find this is the basics and you there are other links as well.
Link is dead. This one works: http://spanish.about.com/cs/grammar/a/whereadjective.htm
Whether an adjective goes before or after a noun depends what is meaning to be said and tradition. I mean the rules of the game. For example, if one was wanting to say, a good man in Spanish it would be, "un buen hombre." If one wanted to say, a great man, it would be, “un gran hombre." And, "gran," here is short for, "grande." When "grande" is used before a noun it is always cut down in size like that. But you can put it behind the noun, also. "Un hombre grande." The meaning then changes because of the different placement. Now it says, a large man, or big man. If you wanted to emphasize this you could say, "¡un hombre muy grande!" A really big man!
If you were using a color the adjective would go behind. "Un hombre azule." A Blue Man.
indianburger, I answered your question a whole year behind the time you asked it. You should already well know the answer now if you had continued with your studies. But I know that at this point in the lessons there are others with the same question rattling around in their heads. Your question needed answering, so did.
"I am writing...." is also a correct translation of "escribo". Context would tell us which would be the correct tense to use. Since there is no context here, only one sentence, I just thought which would be the most commonly used sentence. I figured "I write my own letters" would be something I would say more than "I am writing my own letters", so that's what I put. BTW, because it can be translated both ways, DL usually accepts either the English simple present or the present continuous tense for the Spanish simple present tense.
Since you asked, "cards" is just one of several meanings for "cartas." Many of the words we are learning can have a number of different English meanings. It is not in Duolingo's interest or aim to service them all. This is basic Spanish and is not meant to be all encompassing. It is enough to learn the primary fundamental meaning of a Spanish word then move on to the next instead of getting bogged down contending with all the different ways a sentence might mean or can be said in English. After all, these are Spanish lessons.