„Dalej” is usually used with distance. There are quite a few other usages:
- Prosiłam go, żeby przestał, a on dalej głośno rozmawiał. I've asked him to stop but he was still speaking loudly.
- Przeczytałem ten tekst trzy razy, ale dalej go nie rozumiem. I've read this text three times, but I still don't understand it.
- Wykonałem pierwszy punkt instrukcji, co dalej? I've completed the first point from the manual, what's next?
- Dalej, chłopaki! Go on boys (do x)! -> call to an action
Usually: krok (step) is kolejny (next), poziom (level) is wyższy (higher) or kolejny or następny (but not dalszy). Kroki (plural of krok) can be used with dalsze (declined dalszy) when we think about the actions that are meant to be done in (rather) distant future.
These days "further" can replace "farther" in all situations. There remain other cases where only "further" is possible, e.g. in a non-quantitative sense (furthermore, further point). "farther" is getting a little less common these days but it's still totally valid and is preferred for quantitative contexts in formal language.
In this case, both "farther" and "further" are acceptable. Despite many grammar guides stating "farther for physical distance and further for figurative distance" (not really "things"), there are myriad examples showing that "rule" wasn't really a rule before.
For one example, see: https://meriam-webster.com/words-at-play/is-it-further-or-farther-usage-how-to-use
There are situations where only "further" is acceptable -- when using it as a verb or when talking about something additional or beyond. If you can't measure it (e.g., with a ruler or odometer), then "further" is allowed.
In this sentence, the extra distance we would be going is measurable, so "farther" works. But, we aren't saying "Let's walk 1 km more", we're basically saying "Let's keep walking some more.", so a strong case can be made for "further" being the better choice (which i agree with).
And if this is talking about a relationship, or performing a task, then "further" makes more sense, but either is acceptable. As the second link says, "if there is some confusion between it being a physical or figurative distance, it is now considered fine to use either word."
I would say that isn't just "now" -- they've been interchangeable for centuries. This reminds me of the "controversy" regarding splitting infinitives, or ending sentences with a preposition -- they're recent "rules" created by grammarians to describe how they thought language should be used, but they weren't describing how language is really used.
There's a typo in the first link that i can't fix from my phone -- it should have 2 'r's in "merriam-webster.com":