Help with email etiquette + How do I ask for a research project?

[supastudier2000]

Hello for current and future health care professionals!

I have a question on how to email this grad student that I am shadowing that works for this professor!

Basically, I was told that I would work as a lab assisant for a few months and that I would be given a project of my own to work on after those few months. I worked for a couple of weeks but the COVID-19 situation took everything a way, this was before spring break, I emailed during break and asked if I could do anything to help and the grad student said that he would send me a couple of research papers to read after break. I havent gotten anything from him so I am deciding to email him soon. What I want to get out of the email is...
1) to be able to help the lab if they need it
2) to receive a couple of research papers
3) most importantly, to receive permission to start looking into/coming up with an idea for my own project and start designing it!

I dont know how I would word this to not sound pushy, and not sound like I am demanding a project of my own. I also want to word it in a way that makes them more likely to give me a research project. Should i email the professor directly instead of the grad student? How would this change the wording? ive only met the professor once because he's never in his lab, he's always in his office! I kind of need a research project urgently since I am applying for med school in 1 year.

Thank you in advance!

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[JAK2-STAT3]

Current Research Assistant here. To begin with, I wouldn't wait on a grad student to send you papers. Read what the PI has published. Since you've already worked in this lab for a couple of weeks the PI presumably knows who you are. Try something like this:

Dear Dr. X,

I hope that you and your family are doing well. I greatly enjoyed working with (grad student) in your lab, and am wondering if there will be opportunities to continue this work after the shutdown has ended. We had previously discussed the possibility that I could work on the XYZ project. I am still interested in this opportunity and have been reading publications to see how others have conducted similar experiments. My brief time in your lab was a great experience and I would love to help out in whatever way I can. Please let me know if you think this is possible.

Thank you,

Supastudier2000.

Keep in mind that the institution may be on a hiring freeze and that the PI might not know when the lab will be allowed to return to work. This is the case for my institution. It sounds like they said they had an independent project for you, but you were only there for a couple of weeks. They're still getting to know you and you don't want to come across as too pushy or entitled. The way around this is to express your enthusiasm for the lab's work and show that you are taking initiative to learn more and plan an experiment. That is what I was going for in the sample email. PIs are generally quite receptive to hearing about how cool you think their research is. You don't want to send an email that is too long or gushy but a short email expressing genuine interest and enthusiasm probably won't hurt. Your main goal is to cultivate a good relationship with this PI. If you have a good relationship with them opportunities and good LORs will follow.