Any contract dealing with real estate must be in writing to be enforceable. If you are not going through a real estate agent, you are not required to have a purchase agreement, but it is a good idea. You can obtain the purchase agreement the real estate agents use from the Louisiana Real Estate Commission. See link
The mortgage does not matter as it gives no ownership rights. If the home was in the husband's name only, and there was no will, the property passes to all his children and the step-son can make the step mother leave. If there was a will, the property passes according to the will.
Yes you should buy owner's title insurance. Owner's title insurance is not very expensive especially if you also have to get title insurance with your loan since you get a discount for buying both together. You would be surprised to learn that the United States government, which is self insured for everything else, still buys owner's title insurance when they purchase property.
You, as the executor have an obligation to obtain insurance on the home. You should use succession funds to do so and you must file with the court to obtain court approval to use any succession property. If you need to evict her you have the right to do so.
Your rights depend on if she left a will or not. If she left a will, then your rights are determined by the will. If she did not leave a will you will inherit all of her property. If she and your step father bought property together, you would inherit your mother's 1/2 interest in the property, subject to a usufruct in favor of your step father. A usufruct simply means that he has use of the property.
Your inherited property is separate property and you do not have to let him return. You should obtain a copy of the judgment of possession and have it available to show law enforcement officers should you need to.
If the succession was done properly, the judgment of possession should reflect that all three children are what is called naked owners, and the one child has a lifetime usufruct. Normally if a person is living in the house they can get the insurance on the house. The other owners should ask to be named as additional insured on the insurance policy in case the house is damaged they would be protected. Insurance can be written with other insured parties as most mortgage companies require that...
You should consult an attorney in Germany but Germany is a Civil Law Jurisdiction just as Louisiana and under our law the structure or house is not mentioned in a sale contract in Louisiana either. Under our property law, a structure attached to the land, such as a house, belongs to the owner of the land so there is no need to describe the house as it belongs to the person who owns the land. That is why only the land needs to be described.