How can I file form I-130 before our I-829 petition is approved?

Yes, a conditional permanent resident may file I-130 petitions for each qualifying family member. If the I-829 is denied, beneficiaries will not obtain permanent residence.

Only lawful permanent residents and U.S. citizens can file I-130 petitions for alien relatives/spouses.

Yes; you can file an I-130 petition as a conditional lawful permanent resident. The only family members that would be eligible would be a spouse and/or children under 21 (F2A), these would likely be a spouse or children acquired after you obtained your green card, or an unmarried adult son/daughter (F2B). There is a visa number backlog for both of these categories so it is likely that your I-829 petition would be adjudicated (hopefully approved) before an immigrant visa number would become available for the beneficiary(ies) of the immigrant petition you file. If for some reason your I-829 is denied, the beneficiary would not receive his or her green card.

If the petitioner loses permanent residency before permanent residency is granted to the family member, then their cases will be terminated.

As a conditional resident, you could file a I-130 for your spouse or child, when the relationship was established after green card approval. For example, the conditional green card was granted on 12/01/2014, and you married a foreign national on 01/01/2015. The family member will have a conditional green card just like yours. They will be required to file an I-829, as well. If your I-829 is denied, theirs will be denied too.

Based on our research - it is possible for your spouse on a conditional permanent resident to file a petition on behalf of qualifying relatives while on conditional LPR status. Sec. 8 CFR 216.1 Definition of conditional permanent resident. A conditional permanent resident is an alien who has been lawfully admitted for permanent residence within the meaning of section 101(a)(20) of the Act, except that a conditional permanent resident is also subject to the conditions and responsibilities set forth in section 216 or 216A of the Act, whichever is applicable, and 216 of this chapter. Unless otherwise specified, the rights, privileges, responsibilities and duties which apply to all other lawful permanent residents apply equally to conditional permanent residents, including but not limited to the right to apply for naturalization (if otherwise eligible), the right to file petitions on behalf of qualifying relatives, the privilege of residing permanently in the United States as an immigrant in accordance with the immigration laws, such status not having changed; the duty to register with the Selective Service System, when required; and the responsibility for complying with all laws and regulations of the United States. All references within this chapter to lawful permanent residents apply equally to conditional permanent residents, unless otherwise specified. The conditions of section 216 of the Act shall not apply to lawful permanent resident status based on a self-petitioning relationship under section 204(a)(1)(A)(iii) , 204(a)(1)(A)(iv) , 204(a)(1)(B)(ii), or 204(a)(1)(B)(iii) of the Act or based on eligibility as the derivative child of a self-petitioning spouse under section 204(a)(1)(A)(iii) or 204(a)(1)(B)(ii) of the Act, regardless of the date on which the marriage to the abusive citizen or lawful permanent resident occurred. (Amended 5/23/94; 59 FR 26587 ) (Amended 3/26/96; 61 FR 13061 )Source: 8 CFR 216

You have to have permanent residence in order to file an I-130 petition.

A better practice would be to wait until the conditions are removed, then apply for the I 130.