my chihuahua puppies eat their poop but we give them plenty of food and water.. is it normal for them to eat their poop?

we have a 5 month old chihuahua male. He is very hard to potty train. He just goes where ever he wants to, be it on a bed, on clothes, in his dog bed, in the other dogs bed. everywhere but on the newspaper that I want him to pee and poop. One day he might do it all right and then for weeks do it wrong. any ideas on how to do this? It is getting frustrating.

As i mentioned before im getting a chihuahua in about..... 4 more weeks :3 he's going to be 2 months old and ready to be kept by me.

im just worried because ive taken notice of the weather and its really cold that even makes ME shiver! i'm nervous for my chihuahua, im sure its going to be real cold for him because he has no fur and hes only a baby.

anyone got suggestions for clothes that might keep him real warm? i was thinking of holding him in my arms to make him real warm while im walking him and while im sleeping ill let him sleep on my bed or get him blankets.
if you've got suggestions of jackets and stuff please help to give me the site of how it looks like ^^ thank you for all ur help people (:
i didnt mean carrying him the whole time im walking him. im going to carry him when he gets cold.. ^^ and i wont let him sleep on my bed, u are right. i dont want him to poop or pee on my bed ill just buy him a nice comfty and warm bed in my room :3

toy breeds. What's with that? I fear a vast majority of people who get these "teacup chihuahuas" or "micro-mini diddly do dahs" aren't even thinking of them as dogs....but moving stuffed animals. Then they are totally overwhelmed that they have living things that have minds of their own, eat, breathe, pee and poop and whine and bark and bite. I am just overwhelmed by the LACK of mentality
Diane..thank you for not taking offense..and thank you for your positive comment!! Hopefully some "little dog" owners will heed your words! Isn't it just very very sad? You must particularly be frustrated!

and yes! Pit bull folks too! I don't understand the mentality that goes deaf, dumb and blind over an "underdog" and jumps on a bandwagon!