What are some EA projects for students to do?

Hey Emma, have you considered funneling individuals towards volunteer roles or internship roles instead of giving them project ideas? Charity Entrepreneurship hires interns and requires only a minimum of 5 hours a week, and they currently have a graphic design and digital communication volunteer internship.

Also, starting an Alt Protein Project at one's university seems like a possible project, although it's longer-term and likely needs more than 5 hours a week. Starting a One For The World chapter is also a potential project.

There's also the High Impact Accelerator for people interested in a career in monitoring & evaluation or impact evaluation for global health and development.

When I was last on the job market, I spent a bunch of my free time trying to come up with well-justified cost-effectiveness estimates for a wide array of different interventions across several cause areas. I think something like this technically meets your three criteria, but I suspect it isn’t quite consistent with the spirit of what you’re looking for (i.e. projects that take longer than a week to do and will actually probably have some positive impact). Even though I don’t think my CEAs did anything at all to improve the world themselves, I’d still recommend this to early-career EAs, if only because I thought it was a huge help when applying for jobs at GiveWell and Open Phil (which, for the sake of full disclosure, I was not ultimately offered, though I made it fairly far in the process). Even for people who have no interest in working somewhere like GiveWell or Open Phil, I think doing this trains a lot of important skills: conducting literature reviews, thinking about counterfactuals and measuring counterfactual impact, thinking in terms of DALYs or QALYs, some math… etc., and it just isn’t that much of a commitment, either. I probably spent a few hours a day, most days, for up to week on each estimate, but you could spend more or less as you saw fit. It has an appealing kind of flexibility. Finally, it’s highly scalable — there’s no shortage of things to estimate the cost-effectiveness of, so there’s no reason why tons of people couldn’t all reap the human capital and intellectual benefits of doing this. In the aggregate, I think that itself could have a pretty positive impact, and if someone were to find strong evidence that some previously overlooked intervention was actually competitive with, say, the AMF, that would be a pretty great thing for the EA community to know!

Regarding research projects, I'd recommend also looking at A Central Directory for Open Research Questions. I've also collected a list of several concrete research projects and a corresponding guide. 

Also relevant are posts about Task-Y, which you can also find using the pingback for that post. 

In EA Israel we also have people in the fellowship do a project. It has just started this semester, so I'm curious how that and your program will turn out!

My personal suggestion is to spend those five hours as a freelancing nomad by giving unsolicited support to any charity, business or individual which can provide career capital or simply philanthropic results from your work.

A project which both does good while also allows for the flexibility of reconnoissance and growing career capital. It sounds like you might be best freelancing. The book Surrounded By Idiots puts forth four professional personality types (https://www.penguin.co.uk/articles/2019/jul/surrounded-by-idiots-personality-types-at-work.html - a great system for simplifying choices and predicting business interactions!). I suspect you are mostly blue, in which case simply doing some freelance, unsolicited market research, data analysis or trend analysis for a charity are your best bets in terms of doing good while also maintaining the flexibility of growth (career capital) and autonomy (reconnoissance). You can freelance simply by researching -as you already are doing to answer your question- areas of interest for charities. You can make some assumptions (such as 'all charities need market analysis' and 'all charities lack effective partnerships', both have held true in my experience), or you can outright ask any of your favourite charities and give examples of what you might do for them.

However, if you/your friends are mostly yellow, like me, don't settle on one project; you won't thrive with repetition! As someone who changes focus more frequently than is effective, I found traditional volunteering didn't work for me and, as I was finding my skills, I couldn't commit to long project stints. So I made my own opportunities by doing small favours for my favourite charities. Whatever interest I would be focused on at the time, be it journalism, networking, businesses analysis, marketing or graphic design, I'd do a piece of work for my favourite charities and email them my efforts. At times this wasn't well received but it was no effort on their part to say they didn't want my output. On the other hand, I found some great opportunities to do other odd jobs for charities and businesses and it lead to forming my identity as a networker of c-suite members and free gamification provider for charities; neither of which you can learn if you're committing to a single project for another organisation. However, being your own boss isn't for everyone.