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I have doubt in  3rd statement second part 

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alternate keys can have nul values.

primary keys don't have null values.
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1)for BCNF , dependencies will be of type    super key->any attribute , so we don't care what's there in right side , left side must be super key. if i talk more specific then if prime attributes are transitively dependent on key then relation will be in 3NF and every 3NF is BCNF.

2) this is must condition for 2NF , not for 3NF as even if this is satisfied then still there would be redundancy caused by non-prime->non-prime , which is eliminated in 3NF.

3) unique key is different from primary key.It can be NULL.

https://en.wikipedia.org/wiki/Unique_key

https://stackoverflow.com/questions/9565996/difference-between-primary-key-and-unique-key

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