Current Stanford ESS PhD student here, hope this helps.
1) Is it even worth applying to the PhD program straight from undergrad? I have already identified some POIs but I have no idea if they will even consider taking on someone who's just attaining their bachelor's degree.
Yes. Many (most?) of us started the PhD program without an MS. Some PIs encourage applicants coming straight from undergrad to apply to the MS program (mine did, although I didn't listen), and there might be a few PIs who only take students with an MS. I'd email the faculty you're interested in and ask. Also worth noting, from what I understand, the department doesn't guarantee funding for MS students like it does for PhD students, so I'd encourage you to ask potential PIs if they have funding for MS students. The department makes it pretty easy to transition from the MS program to the PhD program (assuming the PI is on board), so if you can get funded as an MS student, it might be the way to go.
2) Would I be much better off applying to the MS program to gain more research experience before applying to PhD programs?
It depends. Some people choose to get an MS first to explore more research topics and decide if they even like grad school before committing to a PhD. I knew what I wanted to work on and that I needed a PhD for the career I want, so I went straight into a PhD. Plus, I'm older and wasn't willing to take on an extra ~2 years of grad school to get an MS first. It seems like you already have a decent amount of research experience, so if you're certain that you want a PhD and you know what you want to work on, go for it? Although you might be considered a more competitive applicant with an MS... again, kind of depends on the program/PI, I think.
3) Also, in terms of a PhD degree, even though I'm coming from undergrad, is it expected that my research interests and subsequent dissertation topic are set in stone upon applying? I'm almost certain that I want to study ecological restoration and how climate change is influencing the ecology of vulnerable ecosystems, but, who knows, something during my time as a graduate student could rewrite my path.
At least in our department, your general research interests should be pretty "set in stone" when you apply, since you'll be writing about them in your application. Further, ESS is a direct admissions program meaning that you're admitted to work with a specific PI, so your success as an applicant largely depends on whether or not your research interests match those of a PI (although I'm sure there are exceptions). The department makes it VERY challenging to switch labs if your interests end up changing or things aren't working out with your PI. Plus our department is so all over the place, there probably isn't another group working on topics you're interested in (again, there are some exceptions).
I don't think any faculty here expect applicants to know exactly what they want to work on for their dissertation. However, it's possible some PIs only have funding for specific projects and are looking for students to work only on those projects. This is another thing I'd encourage you to ask potential PIs about. When I interviewed, my PI had funding for 4 projects and it was expected that I would work on one of them, and I started working on my dissertation project right away. However, different PIs approach this VERY differently. Students in other groups are expected to develop their own dissertation topic from scratch and use their first couple of years to do so, as Hydrobiogeochemist mentioned.
I can't really speak to any other PhD programs but I imagine my response likely applies to other direct admissions programs? I imagine rotation programs are a different story.