Can an immigrant extend her tourist visa if she is in the process of applying for a fiancé visa?

If you are a U.S. citizen, you can file a Fiancee visa petition on behalf of your fiancee' but she will not be able to change her status from a tourist visa to a fiancee visa status within the U.S. You should consult an attorney experienced in family/marriage based immigration to discuss specific questions related to your case.

She is not eligible to extend her B-2 (Tourist) status if she intends to marry you and you are a U.S. citizen who will be sponsoring her for U.S. Permanent Residency. The B-2 nonimmigrant visa classification is for temporary visitors, not for persons who intend to become U.S. Permanent Residents. Regarding your current employment situation, it would be best for you to meet with an immigration lawyer in a private consultation to discuss your options. You may need to find a co-sponsor to satisfy the I-864 Affidavit of Support requirement.