Is it a good practice to choose my undergraduate research topic on my own? Can I get enough help?
So somewhere I've made a moderators life harder, because I thought your three correlated questions were just one question. I think they probably could be, just incidentally. I'm going to answer accordingly, because when it comes down to it, How To Do It, Will I Have Help and What Are the Downsides aren't just correlated - they're interwoven.

My bias: I did my own projects. As both an undergraduate and a graduate student. This worked out quite well for me, but is not without it's pitfalls.


First, yes, your professor should be able to support you in your research interests - the odds of what your interested in being so far afield from their expertise, when you're an undergrad, is fairly unlikely.
That being said, there are two elements of support they won't have: infrastructure and funding. It's helpful, if you're working on a project, for there to be grad students and postdocs working on similar things. Code you can use. Helpful little suggestions like "Have you read Smith's most recent paper in Journal of Important Things?" That kind of ambient helpfulness isn't going to be there. Similarly, even if you're working for free, its way easier to justify conference travel, a piece of software, or an open access publishing fee if it helps an existing research project.


As I said, this worked out quite well for me - I got good publications out of it, and I got to work on my own stuff. But its a harder road, for graduate school may take longer, and you lack the security of working on an established project. Beyond that, if it doesn't work out well, you don't have an entire lab's worth of effort, papers that might be salvagable, etc.