A search on Google Ngrams reveals that "fitted it to " is not even in the top ten most frequently used groupings, so I would not use 'to'. I'd say 'in my house', 'on the wall', and 'on the ceiling( s )'. 'fit' may be the word for this action in the variety of English you are speaking, so that's OK to use where that variety of English is spoken, but where I live we use 'install' and 'mount' for this.
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A search on Google Ngrams reveals that "fitted it to" is not even in the top ten most frequently used groupings, so I would not use 'to'.
I'd say 'in my house', 'on the wall', and 'on the ceiling( s )'.
'fit' may be the word for this action in the variety of English you are speaking, so that's OK to use where that variety of English is spoken, but where I live we use 'instal