You may be able to make penicillin but I'm not sure how you do that, roughly it's growing mold on food and separating out the penicillin but I'm sure there's a lot more involved to get a working product.
Yes and no. You can get a working product easily. Penicillin was being used at least as far back as the ancient Greeks. It wasn't widely used and not even the people advocating its use had any idea how it worked, but it was used. If you want to change the world, though, you have a much harder problem to solve - scale. For antibiotics to be world-changing, they need to be available very widely and at a widely affordable cost. Especially so if you were doing it 500 years ago as no public healthcare system existed. On top of that, you'd need a very large number of production facilities all over the place because transportation was a lot more limited.
But I think it would be a bad idea anyway even if you could do it. In that scenario, penicillin would be the only antibiotic and there would be no chance of any more. The knowledge and everything else needed for developing other antibiotics wouldn't and couldn't exist, so you'd end up with a pretty rapid development of penicillin-resistant bacteria and amongst the very bad effects of that would be a massive blow to the whole idea of antibiotics. So you'd change the world, but I think probably for the worse.
Which is a problem with any "travel back in time and change things" scenario - the effects might well not match the intention.
For me personally, I can't think of anything. Most of us don't have the required depth of knowledge about any technology
and all the things necessary to suport it to be able to transplant it to c1600. For example, some people here have detailed knowledge of how an internal combustion engine works. Enough knowledge to be able to "invent" the concept in c1600. Enough knowledge to be able to draw a detailed enough diagram to allow for at least an initial attempt at making one. But they wouldn't be able to transplant the necessary material sciences and manufacturing facilities to c1600. Without those, even a perfect blueprint of every aspect of a fully functional ICE is just a picture.
If I had some time before the journey back in time, I could have a go at it. My initial thought would be to find out how to make a hand-cranked printing press with the type set on cylinders. I think that could be made with c1600 technology.