Roosevelt was in no way on the right of the political spectrum.
Depends. On one hand, he supported wealth re-distribution, conservation, and reform. On the other hand, part of him was very aristocratic, his love for Al Hamilton coudl only be matched by his hate for Tommy Jefferson, he was very nationalistic, held quite conservative and prudish social views, loved the idea of the self-made man, and viewed slaughter of the American Indian as necessary for America's eventual rise to greatness (though he was not sympathetic with that, only viewed it as fact. He believed that there was also a follow up to that, in which the native should be encouraged and allowed to participate in new society and should have every opportunity that the average citizen have.). I'm currently reading "The Rise of Theodore Roosevelt".