This sounds to me like a very, very bad idea to pursue.
student in Biology ... he's interested in hiring me ... he will not be paying me for my work
Yes, it can be normal in biology for undergraduate students to work unpaid in labs, sometimes as volunteers, sometimes for course credit. The idea in these cases is that the value the student is providing the lab is nil or negative; any value the lab receives is worth no more than the cost of training provided. In these situations, too, the cost to the student to putting in a few hours work per week is not that high. It can be thought of like a lab course taken in a research lab rather than a standard lab course in chemistry/biology. Even then, there is some controversy over whether these positions should be allowed. My personal position is that it's okay up to a limit, as long as students are primarily learning and not primarily spending their time doing menial tasks.
In any event, this situation doesn't apply to you. You're talking about moving to a different country to work possibly full time for free. Don't do this! This isn't how any of this is supposed to work! Either your potential supervisor is taking advantage of you, in which case you definitely don't want to work with them, or there has been some huge misunderstanding (for example, maybe the professor assumed you're also a student at their university, or will be soon). Someone who is not going to be paying you for your work is not interested in hiring you, they're wanting your free labor.
You expect scholarships or grants? These are almost certainly not available to you. Any worthwhile scholarship or grant program is going to be funding graduate students, who have applied and been accepted to a graduate program. Graduate programs get lots of qualified applicants, and are mostly limited in how many they can accept by funds available. Unless you have a personal connection to someone that's going to give you personally a bundle of cash because they have money to spare and they have a personal interest in you (for example, they're rich and you're their nephew), this money doesn't meaningfully exist. Non-graduate students who are paid to work in biology labs are paid using research grants that their advisors get, usually from the government. If the professor in this lab won't pay you, you've already been denied the only reasonable expectations of funds.
I don't think it's worth addressing issues of visas, that's a likely obstacle but isn't even the most pressing one, which is that this is a very bad idea and won't work well for you.
