1) The chain on the chainsaw was too loose so I had to tighten it.
2) He tried to set me up but my boss <s>uphold</s> supported me and didn't issue me any fines.
It would be more common, and a little clearer, to see something like: "He tried to set me up but my boss knew that I was innocent, so my boss didn't issue me any fines."
3) The weather was too severe so no one wanted to venture <s>out</s> outside.
4) He submitted strong evidence that the <s>producing</s> production of this soap must be ceased because of the potential ecological problems.
5) He felt an authentic joy watching <s>how</s> other people rejoice about his presents.
This makes sense as is, but check your spelling to be sure. There are two words that are pronounced the same but have different meanings. Presents means gifts. Presence is different and is talking about the person's attendance or existence at a location.
6) If you hadn't made a campfire, we wouldn't have set the whole forest on fire.
7) He's similar to his father but <s>unlike him</s>, his father has <s>a huge</s> great dignity, unlike him.