Yes, this does reduce your security. The fact that the seed words were generated randomly becomes meaningless if you use a non-random process to select the seed that you actually use. For instance, it is entirely possible (though very unlikely) that a random password generator would generate a phrase such as "Columbus sailed the ocean blue in 1492". You might say gee, what luck - that is a great password to remember, I'll use that one. Yet, a password cracker that tries meaningful phrases before moving on to random strings will be able to crack this password in the initial phase, even though the probability of randomly generating such a phrase is the same as for any other character string of the same length.

No, this does not reduce your security. You are not choosing a seed to use that is not random, you are still allowing the random number generator to create a seed for you which you then chose. There is still sufficient randomness in this process as the seed is still randomly generated.