1. I usually go to sleep after reading.
2. I usually go to bed after reading.
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Q1: Are both the same in meaning?
Q2: Is 'sleep' in #1 a base verb? Is 'bed' in #2 a noun?
1 -- This sentence means you could be reading and then you go to bed and to sleep -- OR it can mean that you read in bed until you fall asleep.
2 -- This sentence means you were reading and the you went to bed.
Yes, "to sleep" is the infinitive and thus the base verb, and yes, "bed" is a noun (object of the preposition "to."