Hi Marcus! 

The first correct sentence here is (b). I'll tell you why. The question was actually asked in the past and it was asked as follows, 'Where is the library'? Notice that I have given the question in quotation marks '.....'. We call this DIRECT SPEECH. Direct speech brings with it the exact verb tense of the original speech, in this case, 'IS'. When we are reporting in the present what someone said in the past without using quotation marks, we are using INDIRECT SPEECH. Indirect speech is simply reporting in the present what was asked in the PAST and so it changes the original present tense 'IS' to 'WAS'. So 'Where IS the library' (DIRECT SPEECH) becomes, He asked me where the library WAS (INDIRECT SPEECH with no quotation marks).

In your second set of sentences (a) is more correct being the more natural.

When we say, 'I told you TO...'  the word TO should be followed with a positive command, e.g. 

'I told you TO GIVE/TO DO/TO STOP' something. It should not be followed with NOT.

So, the sentence, 'I told you to not turn it off' is quite bad English. You could have written, I told you to leave it on. 

When we say, 'I told you NOT TO...' we have already stated the negative part of our command in the most natural way and so we can simply add 'turn it off'. 

I hope this has been helpful to you,

Thomas Duffy

Marco you could ask about the library either way you have it written, because both "is" and "was" are forms of the past tense, say if talking with a friend. "What did he want to know?" "He wanted to know where the library was." You could also answer "He wanted to know where the library is." For the second set of sentences you can give the command "not to turn it off" either way, however, I told you not to turn it off, would be more common, still either sentence is correct. Please let me know if you have any more questions, and I’d be happy to help you!