Yes. All the children would be considered heirs at law under the laws of intestacy. See related question link provided below.
All her biological children are equally entitled as heirs at law.
Yes. ANYONE named in the will is eligible to be included in the inheritance. On the other hand, if the decedent died intestate (without a will) their property would pass according to the state laws of intestacy. In some states, children by a former marriage would automatically inherit a share. You can check the laws in your state at the related question link.
No
In Idaho, children from a previous marriage are entitled to inherit from their father's estate, unless he purposely disinherited them through a will or trust. The surviving spouse would also have rights to inherit, but the laws may vary depending on the specific circumstances and estate planning documents in place.
Are you asking if your previous husband ought to be legally responsible for supporting your children by your new husband?
No, she never remarried or had lovers (at least as far as we know).
A current spouse would have first claim.
You are not able to get remarried before your divorce is final. If you do remarry before that, then your marriage will not be legal.
The second marriage is invalid, so the children of that marriage are illegitimate. Whether illegitimate children are entitled to a share of the inheritance depends on the law of the particular country involved - which you do not specify.
The term is "remarried" (marriage is a noun, not a verb).
no she is divorced from her first marriage
If your marriage was never registered, then your marriage is not legal in the eyes of the court. You need to get remarried right away if you choose.