It can be incredibly intimidating to reach out to a dev, but it’s the best approach. If you haven’t done it yet, then I would recommend consolidating what it is you want to do. Your description gives a very vague and very nebulous idea, most likely because your idea is just that. It will be difficult, if not impossible, for a dev to green light it.
I can tell you the name is very likely to be off the table. Names and Brand Recognition are extremely important. You could probably make a riff off the name - Faithless, Faithful, Finding Faith, Last Hope, etc. A lot of projects do this and then pin the ‘A __ fangame’ to the end to give it more separation and show omages to the inspiration.
Before you go and spend more energy into what I say below (refining your thoughts and game design) you need to message the dev. Simply ask what their feelings and rules are when it comes to fangames. most likely you won’t be the first to ask.
Summary
I’m a wordy person, so I am going to break down your ideas and give some construction on how to make a tighter argument or how to nail down what you want to/intend to copy. Even if you ask to do something (can I copy myself doing x animation and animate it myself, so it looks similar to yours but isn’t yours) and you don’t use it, they won’t be mad. It’s all about packaging your ideas and intentions as plainly as possible.
So you’re asking for 3 different permissions here. And depending on what it is you want to use, it could be a yes/maybe or a definite no. Like if you ask if you could reuse the deer sprites my educated guess would be that would be more acceptable than reusing say John or Michael.
Maybe you just want the trees, or you want to edit the deer. And you could ask for all three, but it would help if you make a bulleted list of the assets you are interested in using or editing.
This is tricky. Are you talking about the art style? Maybe the music and sound effects? Are you going for that very retro game feel? Maybe the weird Microsoft Sam voice lines?
There are some concept and ideas that are just in the cultural conscience. That’s why 2d Metroidvania is a popular genre, even if it is literally a mashup of metroid and castle vania. Retro style games, Famicon/Nintendo/Atari style retro games are things you don’t necessarily need permission to use.
Another example is Vampire Survivors. The game did very well, and now you’re seeing an explosion on steam of games that don’t have the same graphics or sound, but copy the mechanics to a T. Technically the idea of earning upgrades after killing monsters isn’t unique, nor is the idea of having to face down a swarm of enemies. I am not saying that gives you carte blanche to do the same, or that you could copy Faith’s story beats or action sequences, but if Faith is the only game allowed to use the mechanic of running away from monsters instead of killing them… We have a major issue in the horror game space, lol.