It didn't exist at the time. Mexico fought its war of independence between 1810 and 1821; the Monroe doctrine wasn't elaborated until 1823.
Yes, He violated the Monroe Doctrine by installing Maximilian as his puppet in Mexico..
Yes. The British were the only world power with a navy of significant enough strength to enforce the Monroe Doctrine. If the US tried to enforce the Monroe Doctrine, the Spanish fleet would have easily crushed the nascent US Navy.
Monroe Doctrine
President Roosevelt made it clear that he intended to enforce the monroe doctrine in 1904.
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Monroe Doctrine
The Spanish-American War resulted from an attempt to enforce the principles expressed by the Monroe Doctrine. The United States sought to prevent European colonization and interference in the Western Hemisphere and saw Spanish control over territories like Cuba as a violation of this doctrine.
No country was "aided" by the Monroe doctrine. It was used to replace Spanish rule in Cuba and French rule in Mexico with American puppet regimes.
Monroe Doctrine 1823
The Monroe Doctrine was articulated in James Monroe's Congress.
The Monroe Doctrine was proposed by President James Monroe.
In the early 1900's, the Monroe Doctrine proved it's power. President Theodore Roosevelt aggressively enforced it during the Venezuela Border Dispute and in securing the independence of Cuba from abusive Spanish rule.