Hi Anna,
Nice to meet you. When you got your little guy, did you confine him in a small area or crate train him? If not, then he never realized that the house was not his personal potty. Most canines will go away from where they eat and sleep. That is an born knowledge in them.
Like Mary Lou said, put him back in a small area (gated hallway or very small kitchen). Take him out more frequently, rewarding him with a special treat that he gets ONLY when he goes potty outside. My Ayla was trained to go on wee wee pads and doesn't go outside. If you would like to do this, then give the treat only when he goes on the wee wee pad. Don't give in and let him run the house until you get him to understand that he has to go potty outside or on the pad.
Some people use a bell as a training so the dog rings the bell when it has to go out. This may be a way to get him to do things different. Again, the good treat only when he goes potty outside.
Also, clean your carpets and the spots he goes with an enzyme cleaner product that takes all the odor away. Petastic is a good one. Ammonia or vinegar doesn't get rid of all the urine. Dog's noses are very good and they can still smell it.
Chewing, again, keeping him confined until problems are changed. Give him things he is allowed to chew. If you are using wee wee pads, put them in a holder that they sell so he doesn't get in the habit of chewing them. Don't give things like tied up socks or old shoes... he won't know the difference.
If you don't want to confine him, you will have to leash him to you so that you can keep an eye on him all the time. This way you can stop bad behavior BEFORE he does something wrong. They don't know why you are yelling at them after the fact. You would have to catch them in the act.
I have found that Shih Tzus work better with reward then with reprimand though. Keep that goodie in your pocket so it's right there.
Ayla loves bacon. I can make it into tiny pieces.
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Dee and Ayla