Any property owned by the decedent will pass according to their will or the state laws of intestacy if they had no will. You may have an interest in the property as the surviving spouse depending on the laws of your state both as an heir-at-law and possibly under the doctrine of election. You should consult with an attorney who can review your situation and explain your options under your state law. You can check the laws in your state at the related question link provided below.
The spouse can, but not the children.
That depends on how the property was titled. If the spouses owned as joint tenants with the right of survivorship or tenants by the entirety (as most married couples do) then you have no claim whatsoever. In that case, the property automatically passed to the surviving spouse. If it happens the property was owned as tenants in common then you may acquire an interest in your deceased parent's half along with the surviving spouse providing the parent didn't leave the property to their surviving spouse by will. First check the tenancy on their deed.
If the deed is in JOINT ownership, the survivor gets it automatically. If there is a will, the property goes to whomever it is willed to. If there is no will, the laws of intestacy apply, giving the spouse a share and surviving children a share.
No, the house is in the name of the one spouse. Which is why you MUST make sure you put both names on a deed.
That would depend upon the laws of intestacy and survivorship in Indiana, and the exact words used in the deed. Without looking up your particular state: It may well be that the surviving joint tenant (the daughter) obtains exclusive ownership of the house, as the estate has no ownership of the house to distribute in probate of the intestate. If the daughter and father were tenants "in common", and not jointly, then the father's ownership passes to the statutory heirs by intestacy (typically half to the surviving spouse and half to be divided by all children or their surviving heirs, etc).
The wife and kids.
If you acquired the property as joint tenants with the right of survivorship then you automatically own the property as the surviving spouse. You do not need to record a new deed. You need to record a copy of the death certificate in the land records as notice that the other joint tenant has died. Any professional checking the title to your property will note the joint tenancy recited in your deed, see the death certificate for your spouse and know that by operation of law you are now the sole owner of the property.
Usually in these, cases ownership will go to the surviving spouse.
A Deed of Waiver usually means that a person is formally waiving their rights to something they are otherwise entitled. In a divorce, for instance, some parties agree to sign a Deed of Waiver to waive rights to a spouse's pension after death.
In a situation where spouses hold property as joint tenants with right of survivorship, the death of one spouse makes the property belong wholly to the surviving spouse (subject to any mortgage or liens, etc.) Any owner of real property can quit claim their interest. So, yes. But a warranty deed (a regular deed) is a better way to go, especially when the property is being passed to more than one person, such as the case here. You want the deed to specify how the siblings hold the property, likely as tenants in common.
Both. The property would be in his estate and intestacy laws would apply.
It depends on the laws of your country. In the UK, as surviving spouse - she would be entitled to his share of the property. However - she may want to 'buy out' the son's share in order to have exclusive ownership.