booleans and nulls

Out of curiousity, 

1. Does a boolean column occupy 1byte of disk whether
or not the value is null or not? 

2. Is matching on IS NULL or = 0 more efficient? 

3. If I ix'd columns w/ null does postgres know
whatevers not indexed is null or would their be no
point?

I currently utilize null fields as 'not a value' has
meaning in a program i've been working on as I don't
want to put false in every column when i only need a
couple with a true/false value. 

I'm not joining tables on NULLS, just filtering w/
them. 

Thanks

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