
Ed M. answered 09/29/15
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Help with grammar, French, SAT Writing, the TOEFL and ESL.
A simple sentence has just one independent clause, that is, a clause (i.e., a phrase that contains at least a subject and a verb) that can "stand on its own" as a complete sentence. A compound sentence consists of two or more independent clauses, while a complex sentence has at least one independent clause and at least one dependent clause, i.e., a clause that cannot be a sentence on its own usually because the clause contains some kind of subordinating element like while or because.
Under these definitions, then yes, your example I was scared of trying again and failing for a second time, but I did it! is a compound sentence because there are two independent clauses, I was scared of trying again and failing for a second time, which consists of the subject I and the verb was along with the lengthy subject complement scared of trying again and failing for a second time, and but I did it, consisting of the subject I again, the verb did and the direct object it (but is not a subordinator).
Your example School wasn't always something I was good at is arguably a simple sentence, but it could also be considered a complex sentence if one classifies adjective clauses as dependent clauses, the adjective clause here being I was good at (once again having the subject I and the verb was); an adjective clause, otherwise known as a relative clause, modifies a noun, in this case the indefinite noun something. Instead, if this sentence were changed to School wasn't always something easy for me, for example, it would be unambiguously a simple sentence since there would be only one subject and one verb, i.e., School (subject) and wasn't, actually a contraction of the true verb was and the negative particle not.
Finally, your example Looking out my window also means to me that I got another chance , I got another chance to wake up and tackle the day and be able to do something great actually illustrates an "error" commonly called a comma splice since what we have here are two complete sentences, Looking out my window also means to me that I got another chance and I got another chance to wake up and tackle the day and be able to do something great, joined by a just comma which runs counter to the rules of Standard Written English (though is quite common in less formal writing). If you just stuck a coordinator like and after the comma you would have the legitimate compound sentence Looking out my window also means to me that I got another chance, and I got another chance to wake up and tackle the day and be able to do something great, but undoubtedly this would be criticized as stylistically a "run-on" or overly lengthy or wordy sentence.