[Questions] Should I still apply for graduate school?

My Current Situation:
I am a second-semester sophomore double majoring in Math and Philosophy, and I am thinking about applying to statistics graduate programs. But my current GPA is very unsatisfactory(3.48). I am doing my best this semester to bring it up, but I think the realistic prediction for my GPA at the end of my sophomore year would be somewhere in the 3.5 range.
I am also an international student and therefore it is harder for me to find internships and research opportunities that are outside of my current institution.
I did read some articles about graduate school from various sources. So far it does not look good for me. I found that 3.7 is usually the comfortable GPA for applying for decent graduate programs (top 50 programs), and it is better to have research experience on my application as well. I have none of these right now.

Question about GPA:
Based on my calculation, if I can get a 3.9 or above GPA from this semester to the end of junior year, then I can reach 3.7 at the end of junior year. But this is extremely unlikely. So I think if I work really really hard, then I can bring it to a 3.6 by the end of junior year, and If I don’t work that hard, I would probably end up with a 3.5.
I know that 3.7 is a significant cut off point which is only theoretically possible for me. But what about 3.6? Is the effort worth it to this 0.1 increase in my GPA? How much do 3.5 and 3.6 differ?

Thinking about my goals and options:
I think that my ultimate goal is to do a Ph.D.
My institution offers a 5 year to master program in Computational Operations Research. I am thinking that maybe I can do this 5 year to master program and then apply for another master program in stat at another institution. So even if don’t succeed in applying for Ph.D. programs, I would have 2 master programs to land me somewhere. But the drawback of this option is that the prestige of the undergraduate program at my institution far exceeds the graduate program at my institution. And doing a 5-year master at my institution might not be my best option.
Alternatively,
I can first apply for a master program in stat and then go for a Ph.D. or,
I can apply directly to Ph.D.
Which of these options seem more realistic and reasonable considering my current circumstance?

How to get research opportunities:
I have been surfing on REU and websites of that sort but it is very inefficient since the majority of the programs listed need me to be a citizen or a permanent resident. Is there any other way to find research opportunities?
How many relevant research experience do I need to be competitive in the application process?

Thank you guys so much for taking time reading my questions! Any response to my questions or general advises will be greatly appreciated!

It looks like no one is answering my questions. I think the length of my questions might be a hindrance for answering the questions, and therefore, I will list the questions in a brief manner:

How much does 3.5 and 3.6 differ when one is applying to graduate school given that one has one or two research experience?

Should I do a master before Phd?

Any way to find research besides REU?

Hope this can clear things out a bit, and can get me some responses.

  1. No difference
  2. Depends more on your research, or lack thereof. A Math major should be find for Stats, assuming that you complete whatever pre-reqs are required. (look up a few top PhD programs and see what they have for requirements.). Additionally, not sure two Masters will be of much value. Why not look to a MS in Stats? Many of those terminal programs are cash cows, so if you can afford it...
  3. REU's are federally-funded (US), so usually limited to US citizens. Try to see if you can get a job at a relevant math/stats Lab at your Uni.

Have you looked into the research that the professors at your university are doing? Sometimes they will take on undergraduates as research assistants in their lab groups. There may be an official application process, or it may be as simple as asking a professor if they have any spots open in their lab.

@bodangles It is relatively hard to get math researches at my university. I have looked into one at the beginning of the semester, they said that the spots are full. But I think I can get into some of the researches in other departments since they might need more people to work on the data. Does it still help me if it is research in another area like psychology?

Psychology might not be a great choice but computer science could be.