About noun clause ?

Dear friends and teachers.
I have some doubts on noun clause. Could you please correct the grammar for the following sentences (if any). And for the last sentence, is it possible to put 2 verbs "exists" and "is" side by side ?

That book I bought was very expensive.
Where he studies is the place her father used to teach
= where he studies is where her father used to teach
Where happiness exists is our home = our home is where happiness exists.

Thank you so much.