If we divorce, do I have to give her half of the money from the house?

You inherit the real property as your separate property. You need to be counseled by a lawyer on how to avoid your wife acquiring an interest in the property. She should acquire no interest except through being put on title, refinancing, or acquiring additional equity (other than by appreciation).

No, so long as you keep it completely separate from your marital assets. However, if you expend money on the house during the marriage (mortgage, equity loan, improvements, repairs, taxes, insurance, hoa dues), then she may be entitled to her half of those funds to be reimbursed to her. If you are paying down on the principal of the mortgage during the marriage, there is an argument that she is entitled to some part of the principal and even some part (very small) of the increase in value during your marriage. If you pay all the expenses out of an account that is made up entirely of your pre-marital money and money earned from renting the house out; and no community money (money you earn during the marriage) is ever spent on the home, then she isn't entitled to any part of it or any reimbursement. Keep your records, just in case there is ever a divorce. Also, you could do a very clear pre-marital agreement, properly prepared by attorneys, where you each have your own lawyer representing each of you, wherein she gives up any right to reimbursement of community funds expended on the home as well as any right to any reimbursement of principal paid, and any right to increase in value during the marriage.

No, an inheritance is separate property, and will be yours and yours alone. However, if you spend money earned during the marriage on that inherited property then your spouse will be entitled to reimbursements, but not an ownership interest.

Inheritance and all property acquired by the parties pre-marriage is separate property. Unless you gift her a share of the home or the community is paying principal reduction payments on the house, then the community acquires no interest in the property. If this is a concern, however, you might want to obtain a prenuptial agreement before getting married so that it is clear what is and is not your separate property.