мне надо написать где infinitive где ing form и где infinitive без to​

ошибки и их исправления выделены жирным

(можно добавить: Sir Arthur) Conan Doyle is a British writer, former physician and an author of numerous adventure books who was born in Britain. Conan Doyle wrote one of the most famous books in the world, (<= нужна запятая) "Sherlock Holmes", (<= нужна запятая) and came up with such interesting characters as Sherlock Holmes and Dr. Watson.

Agatha Christie is a writer who wrote (убрать артикль a) very famous detective stories, (<=нужна запятая) such as Jonah and The Secret Adversary.

I love to read adventure stories because I like them. You learn a lot of interesting and exciting things from adventure books (<= конструкция предложения была неправильной). When you read a book like that, you can travel with the book's heroes and live through the same events that happen to them. (<= конструкция была неправильной, надеюсь, ничего, что я чутка переписал))

I know a lot of adventure and detective books: (можно добавить: for example,) «Count of Monte Cristo», «Сaptain Nemo», «Three Musketeers», «Mousetrap». My favourite book is "Sherlock Holmes". The creator of this book is Arthur Conan Doyle (неправильно был указан автор), who is a very popular writer.