A person vowed to slaughter a sacrificial animal. Is he permitted to eat from it?
If the vowed sacrificial animal was for the sake of Allah, and the one who vowed didn't specify then its meat should be distributed only among the poor and needy similar to distributing Zakah of Al-Fiter so neither him nor his dependents permitted to eat from; however if his vow was to made a banquet and invititing his relatives and others; then he must bring up as much as he can from its meat for them. In addition, he is permitted to eat from it in a reasonable basis. And Allah Knows Best.
Is it permissible for a woman to say that she loves her husband more than her father?
It is impermissible for her to say so since this would hurt her father deep down. Allah, The Almighty, Says in this regard (What means): "And that ye be kind to parents." [Al-Isra/23]. Saying such a thing to her father isn`t an act of kindness since she should keep it to herself even if she felt that way.
Is it permissible for the woman who is observing Iddah after her husband`s death to sit with her daughter`s suitor, although their marriage contract hasn`t been concluded yet?
All perfect praise be to Allah the Lord of The Worlds. May His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
A suitor who hasn`t concluded the marriage contract isn`t a Mahram*, so he must be treated as such. And Allah The Almighty Knows Best.
* The period a woman must observe after the death of her husband or after a divorce, during which she may not marry another man.
* In Islam, a mahram is a member of one's family with whom marriage would be considered haram, concealment purdah, or concealment of the body with hijab, is not obligatory; and with whom, if he is an adult male, she may be escorted during a journey, although an escort may not be obligatory.
Is it permissible for us to sever ties of kinship if our blood-relatives` gatherings/meetings involve acts of sin?
Observing kinship ties is obligatory, and paying your blood-relatives a visit causing their sinful acts to be hindered , then you should do so. However, if their sinful acts continue while you are at their gathering and they didn't respond positively, then observing kinship ties via telephone and the like will suffice in this case. And Allah Knows