About one sixth of all words in English are derived from German. However, of the words used frequently in English, almost half of them are derived from German. Modal verbs and gerunds also have a German influence. However, it has been 1000 years since English split from Germanic languages (1066, precisely, the date of the Norman invasion of England). The grammar is much changed between the two and there has been much influence of French. Consider English as half-way between French and German, with gender endings dropped. [It's a running joke that English got its start as an attempt by Norman soldiers to get dates with Anglo-Saxon barmaids.]

German and English both derive from a much older language. However, English is also mixed with Latin and Greek. Anyway, they are different enough to qualify as two separate languages with two different ways of learning each.

English is a germanic language like german, dutch, swedish, norwegian, danish, icelandic and many other languages. All these languages share some similarities in grammar and vocabulary, but this doesn´t mean they are mutually understandable. English borrowed many latin words and 60% of its vocabulary has a latin origin. Other germanic languages have very few latin borrows, this makes already half of english vocabulary very different from other germanic languages. Besides, germanic languages have split from a proto-germanic language many thousands years ago (more than 3000 years ago), so even the germanic words in english can be very different from german. The closest language to german is dutch (dutch is also the closest language to english, although they are not mutually understandable), german is also similar with scandinavian languages (although they are also not mutually understandable), scandinavian languages are very similar between themselves and are mutually understandable (except icelandic). English grammar is more similar to dutch and scandinavian grammar, but is also similar to german, except for not having declination cases (although old english had declination cases).