1. It is strange he hasn't married with all his money, and him so fond of children. GOOD. The final clause basically means 'considering that he is so fond of children' 2. How could the room be cleaned, and me with rheumatism. GOOD, somewhat old-fashioned construction, similar to 1. final clause = 'considering that I have rheumatism' 3. With very short intervals of sleep, and those entirely filled with dreams. GOOD CLAUSE, but this is not a complete sentence, i.e. there is no subject/verb. 4. Integrity was in the tower, and decision. MAKES NO SENSE on its own. It might be possible to construct some very specific context in which it would make sense.

1. This sentence contains a very rare and advanced structure in "him so fond of children." This is essentially concessive: although he is so fond of children. The first part, "it is strange he hasn't married with all his money" means it's strange THAT he hasn't gotten married, despite having so much money. 2. Here as well, we have the same type of structure in "me with rheumatism"— despite the fact that I have rheumatism. 3. Something similar is happening with "those entirely filled with dreams"— it is like "even those were entirely filled with dreams— meaning that they were not good intervals of sleep. 4. This is incorrect, since "decision" is not something we typically think of of being in a place. We also wouldn't use a comma before and in this particular case. I hope that helps.