You can look for relief in British publications, which follow the rule you find more logical. You are not alone in objecting to the American convention. A whole group of kindred spirits is lurking on one of the links from the N.C. State Online Writing Lab homepage. The American system wins out, but the British system has surprising support. The analysis covers the reasons for the opinions.
Question marks are a little more complicated.
They are placed inside of quotation marks when they are part of the quoted matter. Problems arise when the question mark attaches not to the material inside the quotation marks, but rather to the frame of the sentence. Once is more than sufficient. Twice is regarded as supercilious. The direct answer to your question is yes.