Is the nikah between the woman and her two husbands valid under Islamic law?

Assalamun alaikum, I know a woman who has two girl kids with her first husband. Latter she ran away with a second male few years back. She says ( we doubt her as she is not telling exactly the truth ) she married to that 2nd person , while the 1st male – his original husband was alive and no talaque or qula was pronounced. She separated from the 2nd male also due to some misunderstanding, but she never came to the first husband and mean while her first husband expired. Now again she and the second man started living together. The girls are in our care, and she wants to take them. This is a short back ground. May I know the following under the light of Quran & hadis , what is the fatwa of the esteemed Ulamas :: 1. whteher the nikah between a husband and wife is still valid if the wife or the husband OR any one have illegal relations out side ? 2. Is the nikah with the 2nd male valid, as no talaque or qula was pronounced with the 1st male ? 3. We don’t know actually the nikah has taken place between the 2 nd man and the lady, as the lady is not telling exactly the truth. As an outsider, but just to avoid a sinto be continued between them , can we interfere in this matter ? And can we suggest them to get marry again? 4. Or what is to be done ? 5. Can we send their minor daughters along with the mother, if she insists?