I just downloaded a zip file of .png banners and arrows. However, they were all created black. Is there any way I can change the color of the objects in Adobe Illustrator?
Note that a PNG in Illustrator is seen as one object. There is no mechanism to allow a user to color individual pieces of a PNG within Illustrator. You could use Image Trace to convert your PNG to vector objects. Results are highly dependent upon trace settings and the original artwork.
To work with the PNG as a whole...
Embed your PNG into Illustrator and use
Edit > Edit Colors > Adjust Color Balance. This will allow some overall "toning" of the png.
Note you must Embed the image, not link to it. Simply opening the image with Illustrator will embed it. You can also highlight the image in the Links Panel and embed the image from there.
If you want accurate, specific, areas recolored without tracing, Illustrator is not the correct tool to use. Photoshop, or any raster image editor would be a more appropriate tool.
Yes. When you import (place) a png file (or any raster image format) just turn off the "link" checkbox.
This will enable the "Filter" Menu for that image and you can use adjust colors and other filters to manipulate the image. Just remember that the image will be inside the AI file.
If the "link" option is enabled, you do that in the original file with an external program.
Edited: Here is an image. (off an old version of ilustrator)
As easy as 1-2-3. enter the hex colour you want for the image. I changed a single coloured image to another color.