I want to create a Horror Game for either PC or Mobile, but I don't know where to start.

1. What is the design process for developing a Horror Game, for example; Planning, Research, Ideas etc?

Omniscient, your first question is a programming question - not a game design question. Your second question is a game design question, so your post will remain here in Game Design. For the information of future responders to your post, any replies about engines will be deleted from this forum. Omniscient, you can ask your engine question in the Beginners Forum.

2. The design process is exactly the same as for any other genre. Ideation and research can take place concurrently, and research should continue throughout the design process. "Planning" is not part of the design process, assuming you mean planning the development process. If that's what you mean by planning, then that is a Production topic (you should ask about project planning in the Production & Management forum). 

A lot of books have been written about the design process, but I confess that I have not done a lot of reading on that. I have usually done my design work by the seat of my pants, trying out various ideas until the best one makes its way to the top. I'm in favor of paper prototyping, but if you're comfortable with Unreal, perhaps you can quickly prototype in Unreal. 

Horror games are supposed to not only scare the player and/or make them feel uneasy, but also be fun and challenging in some sort of way.

For example, If your horror game takes place in a mansion setting, try adding locked doors that require keys, and puzzle solving elements. You can even add some Metroidvania elements if you wish.

As far as the scare tactics, try to make your environment as 'uncanny' as possible. Don't try to make it 'scary', meaning don't just make everything edgy and black and white, or put skeletons and cobwebs all over the place, or words written in blood, because it isn't really that scary. Good examples of uncanny environments would be rusted walls and asbestos and mold coming out of the walls. Make the environment seem hazardous and 'off limits'.

That will build up tension, so when the player turns around and sees some wide eyed freakazoid staring at them from behind the closet doorway, it will spook their pants off.

The process of horror game development will be same as other game development but the planning will be different, because the content, character and the idea will be different for other gaming and horror games. Sound design both are equally important to provide a feel of horror game and keep in mind that horror games make the player vulnerable, exposed, and often helpless.

Horror game should also have the background and environment like its isolated, so plan your visuals and space accordingly.  Design everything keeping horror scenario in mind.

Horror games are a hit, be sure to think it through but not overthink it, it has to stay simple and entertaining. And scary ofcourse