Learn Hardcore Chinese: tā bù zhīdào zěnmebàn, wǒ jiù gēn tā qù gōngyuán liáotiān. - She doesn’t know what to do, so I went to the park with her to chat.

It links the first clause (the reason/situation) to the second clause (the action taken) and adds a nuance of “so/then, promptly/as a natural response.” It suggests the action was taken readily or decisively.

Can I drop 就, or put it somewhere else?

Dropping it: Grammatical and natural, but you lose the “prompt/so then” feel: 她不知道怎么办，我跟她去公园聊天.
Placement: The most natural spot is after the subject: 我就跟她… You can also reorder other parts (e.g., 我就去公园跟她聊天), but keep 就 before the main verb phrase it modifies.

Why use 跟 (gēn) here? Could I use 和 (hé) instead?

Here 跟 means “with” (accompaniment) and is very common before verbs of movement or interaction: 跟她去, 跟他说.
和 also works (我就和她去…), but 跟 is a bit more colloquial and frequent for “go/do with someone.” In formal writing, 与 is another option.

Does 跟她去 mean “go with her” or “follow her”?

In this structure it means “go with her.” If you wanted “follow,” you’d typically say 跟着她去 (gēnzhe) or 跟在她后面去.

Could I say 陪 (péi) instead of 跟? Any nuance difference?

Yes: 我就陪她去公园聊天. 陪 means “to accompany (to support/keep company),” highlighting a supportive role. 跟 is neutral “with.”