May Allah increase your reward and have mercy on your husband; may He grant you patience and help you to raise your children.
The answers to your questions are as follows:
Whatever your husband has left behind of wealth, property, a business and so on belongs to his heirs, who are: you, your two children, your husband's father or grandfather, and also his mother or grandmother if they are still alive.
Your portion of his share in the gas station - and any other wealth he left behind - is one eighth, and the rest goes to your children, unless your husband's father is alive, in which case he has one sixth, or if his mother is alive, she has one sixth. The grandfather takes the father's share if the father is not alive, and the grandmother takes the mother's share if she is not alive.
You have to look after your children's wealth and you should invest it in a way that will benefit them. It is not permissible to give it to them until they reach maturity. See the answer to question no. 13262
Your kindness towards your husband's family is a righteous deed, but it should be from your wealth and your share of the gas station. It is not permissible to give it from your children's share, because the one who is looking after an orphan's property has no right to give charity or gifts from it.
You should not ask Allah, may He be exalted, to let you remain a widow, because this is contrary to what is encouraged in Islam. Rather you should get married, and ask Allah for a righteous husband, because of the many benefits and noble purposes of marriage, which include: seeking to have righteous children and form a Muslim family; protecting oneself from falling into haraam or into the traps of the Shaytaan; and strengthening the bonds between Muslims through ties of marriage. If someone proposes to you who is religiously committed and of good character, and you think it most likely that he will take care of your children and help you to bring them up, then you should accept him. This is better for you than remaining without a husband, especially at your age and in the country where you are living.
Sponsoring orphans, bringing them up and helping them are among the greatest means of drawing closer to Allah, and they are a means of being with the Prophet (blessings and peace of Allah be upon him) in Paradise.
It was narrated from Sahl ibn Sad that the Prophet (blessings and peace of Allah be upon him) said: I and the one who sponsors an orphan will be in paradise like this- and he gestured with his forefinger and middle finger (to signify closeness).
Narrated by al-Bukhaari, 5659
It was narrated that Abu Hurayrah said: The Messenger of Allah (blessings and peace of Allah be upon him) said: The one who sponsors an orphan, whether it is a relative of his or not, he and I will be like these two in Paradise, and Maalik pointed with his forefinger and middle finger.
An-Nawawi (may Allah have mercy on him) said: With regard to the phrase whether he is related to him or not, related to him means if he is a relative, such as his grandfather, mother, grandmother, brother, sister, paternal uncle, maternal uncle, paternal aunt, maternal aunt, or other relatives. Or not (related to him) means if he is a stranger (a non-relative). Sharh Muslim, 18/113.
See the answer to question no. 47061
There is nothing wrong with you benefiting from Social Security and using that money to go for Hajj, so long as you are entitled to it according to the conditions laid out by the government.
If a person dies in a car accident, there is the hope that he will be a shaheed (martyr), because he is like one who dies beneath a collapsed building. Please see the answer to question no. 45669
There is a difference of scholarly opinion concerning women visiting graves. Some of them say that it is permissible, some say that it is makrooh (disliked) and some say that it is haraam (prohibited). If you refrain from doing that, that will be better for you and more on the safe side, especially in this situation you describe, when the calamity is still recent. Such actions will stir up your grief again and may cause you to do something that is contrary to Islamic teaching.
Please see the answer to question no. 8198
There is nothing wrong with your children visiting their father's grave, because visiting graves is mustahabb (encouraged) for people other than women.
You must pay close attention to your children at this age, and bring them up with good morals and values. Teach them to memorise the Book of Allah, may He be exalted, and to love good; make them get used to offering prayer regularly. You should also get in touch with Islamic centres and some righteous sisters; this will be very good for you and your children.
We ask Allah, may He be exalted, to help and guide you.
And Allah knows best.
Reproduced from Islam QA