A new assistant hired by Mr. Burns who is jealous of Smithers' position could be the main antagonist. This new character might try to undermine Smithers at every turn.
One idea could be that Smithers finally decides to confess his true feelings to Mr. Burns in a very emotional moment. Maybe after saving Mr. Burns from a dangerous situation at the power plant.
One popular Burns Smithers fanfic could be about their relationship in a different work setting, like if they were in a modern startup instead of the Springfield Nuclear Power Plant. Another might explore what would happen if Smithers finally got the courage to confess his true feelings in a really emotional way.
Archive of Our Own (AO3) is a great place to start. It has a large collection of fanfics on various topics, including Burns Smithers ones. The site has a good search function that allows you to easily find what you're looking for.
I have no definite idea. It might be a comic that focuses on the humorous and unexpected situations involving these characters and the blushing element adds an extra layer of intrigue.
Mr. Burns might try to take care of him. Despite their strange relationship, Burns could feel some sense of responsibility or concern for his loyal assistant.
Mr. Burns would probably visit. After all, Smithers is his loyal assistant, and Burns would be lost without him. He might come with some strange 'cure' he heard about.
Hot water burns would cause a burning pain. After the hot water came into contact with the skin, the heat would be quickly transferred to the skin cells, causing thermal damage. Although burns might only affect the superficial layer of the skin, the injured would feel a burning pain because of the rich nerve endings in the skin, which made them sensitive to pain. When dealing with burns, you can rinse or soak the wound with running cold water, or you can use ice to apply cold compress to the area to reduce pain and swelling. It was not recommended to directly touch the ice on the skin to avoid low temperature damage. Under the doctor's guidance, you can apply an appropriate ointment to promote wound recovery. There may be short-term skin hyperchromation after burns, but it usually does not affect normal life and will gradually subside.
There might be such fanfiction out there, but it could be quite niche. If it exists, it may be in the more specialized sections of fanfiction communities. You may need to dig deeper by using specific search terms within those platforms and also checking related tags.