Question about “even if…”

Hi all, in the following three sentences:

私は本を買っても、読みません

雨でも出かけます

寒くても行きます

The “even if” form is made in three similar but different ways: in the first sentence there is も following the て form of the verb, in the second there is でも that follows the noun 雨 and in the third sentence there is ても that follows the adverb 寒く.

Could someone help me to understand if these three cases come from a unique rule, or if they are different cases to which are applied different rules? Thanks!!

by RioMetal

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