First, you have to narrow down what you mean by “grad school.” I don’t think you mean “professional school” (law, medical, dental,…), but admission to PhD program is very different from admission to MS/MA program. It helps members here to answer your questions if they know what you want.
The first thing to do is to read the information re. grad programs on universities’ websites. Different schools have different requirements/rules/philosophies.
For PhD admissions, research experience, letters of recommendation, GPA, and GRE scores are important, more or less in that order.
For PhD programs, the info is mostly correct, except maybe for the number of students accepted. The number of students accepted depends on the size of the school, the size of the department, the availability of potential advisors, and most importantly, the availability of fund (which no one outside the department knows, nor can anyone predict).
Last year my D was admitted to a PhD program at Cal, along with 3 others. This was only her sub-field. The whole department (a large one at Cal) admitted about 30 people, about half of which matriculated. This year 7 were admitted to her sub-field (almost doubling).
The reason the GPA needs to be high is competitive nature of the admissions process. The pool of applicants is full of people with high GPA. You don’t have to have 4.0, but it’s difficult for ad. com. to admit an applicant with low GPA than others. Read this: https://people.eecs.berkeley.edu/~jrs/apply.html
The first thing to note is that grad admissions committees don’t care about “extra-curricular activities,” except when the activities are closely related to the field you’re applying for.
“At least a year long” research makes sense, and is possible. My D entered Cal as a freshman, and started her research the very next summer. Her research lasted until she graduated (in 3 years). To become a research assistant at Cal, you need to be proactive. Do not wait until the position is posted; by then it’s probably too late.
My D got her research position by talking to a professor after attending his presentation at a seminar. He didn’t have any position open, thus introduced her to another professor. This professor in turn introduced her to a post-doc he happened to talk to the day before (the post-doc was not this professor’s advisee) who was in need of an assistant. The position she got was never posted. She stayed with the research for almost 3 years, even after she graduated, then left to start her own.
From what I know, the funding has nothing to do with your GRE scores.
Note that decent PhD programs always fund students (tuition + health/dental insurance + 20K - 25K per 9 months of the academic year). Funding for MA/MS programs is less “generous” and depends largely on the program.
Best wishes to your journey.