Learn English – the difference between “okay with” and “okay for”

The preposition within has nothing to do with the ordinary sense of the preposition with = “accompanying, alongside, by means of, etc.”. Within means “inside” in spatial, temporal and figurative senses.

The hoard was discovered deep within the mound.
You must respond to this communication within thirty days.
They are within their rights in refusing to be interviewed.

Consequently, within is not a valid translation of German in in this context. However, English does support both German uses: you may use either with for mit or in for in.

With this option ...
In this option ...

• HISTORICAL NOTE, for those who wonder why the compound with + in has this meaning:

  Old English wið (cognate with German wider) originally meant “against, by, back from”, and the modern sense of with was expressed by mid (cognate with German mit). In the later part of the Old English period, however, northeast England was occupied and to some extent settled by speakers of Old Norse dialects, and over the next centuries (down into the Middle English period) many Old Norse words replaced the corresponding Old English words. For instance, they and are are of ON origin. Old Norse við, a cognate of with and wider, had approximately the sense of mid and mit, and under its influence, with shifted to the modern sense. However, the old sense lingered in established compounds such as withstand (stand against), withhold (hold from), withdraw (draw away from)—and within (against or by the inside).

Is "assist in" the same as "assist with"? Can I always substitute the one where the other is used, or is there a difference in meaning?

In general, they're pretty similar and frequently interchangeable -- at least one-way. (You can say "assist with" for "assist in," but you should be careful swapping "assist in" for "assist with," since there are some nuances.

If you "assist in," it may indicate a longer-term and/or more in-depth assistance -- the senior academic meeting with the junior one daily over a course of months, for instance.

If you "assist with" something, it can indicate a much shorter-term, or "shallower" form of assistance -- you aren't going around asking questions to help the police, but are instead answering the questions the police gave. (If you said "I am assisting in the police inquiries," you would be presumed to be doing a share of the work.)

So you can assist your co-worker with a project, or you can assist your co-worker in his work, and it means pretty much the same thing. (Though even there, notice the nuance: a project is a thing with an end, while "his work" is more open-ended!) But you want to be careful saying you're assisting the police in their investigations unless you mean that you're doing more than just answering a few questions.

However, even if you use the "wrong" in/with, a sentence in context will usually be interpreted the correct way.