That would fall under “research” if it was the sort that would result in papers, and would certainly be a useful indicator to me as a PI hiring students. Internships where the student did more standard, BS-level tasks are much less useful.
Expensive equipment is fairly irrelevant. If I have no similar equipment, then it doesn’t make a lick of difference whether or not the student has used it or not, and if I do have similar equipment, I pretty much just assume I would have to train a student on it anyway. Equipment training is easy. I’d rather have a better feeling about whether or not the student has the drive and quantitative skills required to succeed in a research setting rather than their ability to be trained to use equipment.
This can vary. Undergraduate professors are probably the single best source of information on this topic because they have all been through this process and have hired graduate students for their own labs, so they have a pretty good idea of what it takes to stand out and succeed.
Other than that, once a student knows what they want to study, they can browse the relevant scholarly journals for specific topics that interest them and use that to form a list of programs active in that research area.
Maybe a little, but how am I to know that another equally-qualified student could have earned the same scholarship but just didn’t know about it or how to apply? They certainly won’t hurt, but they don’t move the needle much for me personally. Most of the time it seems they are based on high school grades and achievements anyway, which aren’t really relevant to graduate admissions.