Is there database for for patent lawyer customer numbers in US?
I don't believe so. Patent practitioners have a registration number which is publicly searchable at the USPTO (as you have found). However, I do not believe there is any way to search by customer number.
An an aside, the customer number is used to appoint a firm of attorneys to act for you, rather than a single named attorney (MPEP § 403).
What rights does a power of attorney give?
37 CFR 1.32(a)(2) provides:
Power of attorney means a written document by which a principal authorizes one or more patent practitioners or joint inventors to act on the principal's behalf.
In other words, the power of attorney gives your attorney the right to act on behalf of the applicant. Most notably, this means that they can respond to the office action, and it's treated for legal reasons as if it comes from the applicant.
Can the attorney make decisions without consulting me?
Not really. The power of attorney allows the attorney to act on your behalf, so in theory they could act without consulting you. However, in practice this should not happen. Ethically, an attorney can only act on your instructions. They cannot make decisions on your behalf.
To respond to this office action do I need to sign power of attorney?
Yes—if you want your attorney to respond to the office action, you (as the applicant or a representative of the applicant) will need to sign the power of attorney. If you do not, the attorney will not be able to validly file a response.