Saying thanks in the personal statement?
No, a statement of thanks in the form you have described has no place in a statement of purpose.

The statement of purpose should be a concise, focused document. Everything in there should be there for a specific purpose: to convince the readers that you would be a strong addition to their department. Anything that doesn't serve that purpose distracts from that purpose and doesn't belong in there.


  The personal statement should give concrete evidence of your promise as a member of the academic community, giving the committee an image of you as a person.


None of the things you have written in your thanks "give concrete evidence of your promise as a member of the academic community" so they do not belong there.

Besides for being ineffective as part of your application for graduate admissions, it's also somewhat ineffective as an expression of gratitude. Private thanks expressed to the person you are thanking are nice; public thanks (like in a thesis, or a Nobel prize acceptance speech) are also nice. What's the point of thanking someone in a private document, that they're not the intended audience of? If you want to thank your mom, send her a letter, or call her on the phone and thank her.