Imagine I am the last surviving human, what should I do for the civilization within the rest of my life?
Assuming you've not taken on the ability to asexually reproduce, civilization no longer will exist.  To survive, I suggest you brush up on the following skills:
* Gardening to grow your own food.
* Hunting or fishing including to know how to properly field dress your game.
* Finding safe and stable shelters to live in.

I also suggest that you get a dog to help protect your homestead and alert you to dangers.
What sort of dangers should I watch out for? For example unmanned nuclear reactors might cause issues
As the last surviving human, you would need to be aware of various potential dangers, both immediate and long-term. Some of these dangers include:

1. Unmanned nuclear reactors, as you mentioned. If these reactors are not maintained properly, they could fail and release radiation into the environment, causing harm to you and other living beings.

2. Natural disasters such as earthquakes, floods, and wildfires can pose a significant threat to your safety and wellbeing.

3. Wild animals that are accustomed to living in a world with humans could become more aggressive or dangerous, as they may no longer fear humans.

4. Disease or illness can pose a significant threat to your survival, as you will have no one to turn to for medical assistance.

5. Accidents can happen, and without anyone to help you in case of an emergency, you must be careful and cautious in everything you do.

Overall, it's important to remain vigilant and cautious, and to be prepared for any eventuality.
Wouldn't there be almost no disease or illness since there are no humans left to spread it?
Many germs can infect or be carried by many more creatures other than humans, or even survive by themselves. They can access you as the last human in multiple ways. For example:
- Insects. Mosquitoes of different species and habitat can spread many different diseases such dengue fever, yellow fever, and Japanese encephalitis. Flies are no better with sleeping sickness, onchocerciasis and many more. Without a functioning society to control insects, this could become a big problem.

- Water. There are waterborne diseases such as Cholera and Nematode infections caused by swallowing contaminated water, food or beverages. This could become worse without humans, since there would be nobody to operate water treatment facilities.

- Animal contact. Contacting with the saliva, blood, urine, or other body fluids of an infected animal can cause diseases such as Rabies.