Do Australian skilled immigrants have to go through an intermediary? What are the good intermediaries?

You don't have to deal with skilled immigrants through an intermediary. If you meet your requirements, your language ability is strong enough, your hands-on ability is good, and you are willing to bother with those materials, you can do DIY yourself. There are many people.

There is no way to recommend a good intermediary, there are so many intermediaries in the country.

However, as far as the current situation of skilled immigrants in Australia is concerned, according to the four requirements of IELTS 7, the language level of qualified people will not be bad. I don't know if your conditions are enough.