Learn English – for reminding VS in reminding

In your first question, you do not need the for. Examples:

I appreciate your assistance filling out the form.
I appreciate your assistance finding a job.
I appreciate your help cleaning the garage.
Or for a simpler case like the exact one you posted, I appreciate your assistance moving.

If for some reason you really want a conjunction there, you could use in for many cases, but it's not necessary. However, it's worth knowing as many people use it. Example: Thank you for your help in cooking dinner.

In the second question, the order of someone vs. me will depend on what you're trying to convey.

someone in touch with me implies the person you are speaking to told this someone your information and that someone contacted you. me in touch with someone is the reverse: the person you are speaking to gave you the someone's information and you contacted this someone.

It's all about who contacted who: X put Y in touch with Z. To put it another way: X enabled Y contacting Z. X is implicitly the person you are speaking to, ie, "you".

Accuracy refers to the degree of correctness or precision of some action or by extension of that which performs the action.

The rockets returned to their landing platform with great accuracy.

We can speak of accuracy as an abstraction, as a quality of actions or things that perform actions. But in actual contexts it does not exist apart from the action or the thing taking the action. So it is not idiomatic to say:

We need to improve the accuracy to detect such errors.

—not unless that sentence is understood to be elliptical:

We need to improve the accuracy [of our detecting device] to detect such errors.

So that if we were to say

In order to detect such errors, we need to improve the accuracy.

a reasonable question would be "The accuracy of what in particular?" if the thing that can be accurate in its action was not already known from context. But if it is known, the sentence is elliptical, as above.