Alfie: What's it all about?

About a month ago me and my partner got an eight-month-old Shih-tzu cross - Alfie. A friend at work bought him when she was drunk - she got the impression that he was just going to be abandoned.
She only had him for the weekend before giving him to me (as she couldn't cope). Although my partner has always had dogs as a child, I have never had one. I am a dog lover, but really don't know what I'm doing.
When we first got Alfie was very unsettled and my partner (who was then out of work) couldn't leave him alone. He would bark constantly - we live in a flat and we worried about the sound. My partner now has a job, we both have to leave before 6 am, so we started taking him to my partner's mum on the way to work - as she is not working. Whenever she went out and left him he would wee and/or poo - sometimes on mats left for him, but not always.
My partner's mum recently went away for a few days, so I took his cage over and put him in it while I was at work - he had his food, some treats and a couple of toys in with him. He went mad when went to pick him up. He had made a right mess - his water was all tipped over there was food everywhere and the treats were outside the cage. The next day when I went to pick him up - he greeted me at the door - he'd got out!! He had chewed off three of the bars! A neighbour lent us their cage which seemed much stonger - but he still managed to chew off on the bars on that cage too. I don't want to use a cage anymore as I'm worried about him hurting himself. He obviously is really distressed whenever he's left on his own - but we have to go to work. He still has his balls, but we are hoping to get him neutered very soon - but I don't think that will stop his anxiety. I also would like to be able to leave him at home, and not keep moving him around. Please can you help, how do we stop this behaviour?
Sally Neatham, by email