What is the ruling on using images from the internet on a personal website for explanatory purposes? Is permission required, and must the source be mentioned? What if the source contradicts Islamic law? Is it permissible to hand-draw images that are identical to them?

Internet websites were created for people to benefit from them, and this includes reading their content, quoting from them, and republishing. There is no harm in taking pictures, information, and fatwas from them, provided the matter is attributed to its source. The situation here is similar to dealing with books, newspapers, and magazines. If the quotation is verbatim without alteration or addition, it must be attributed to its owner if it is intended for republication. However, if the source is one that should not be referenced due to its dissemination of vice, then it is preferable not to take from it. If something is taken from it, then it should not be referenced directly. In such a case, it should be mentioned that it is "quoted" without stating the source itself, out of academic honesty. As for manually redrawing or replicating such content, there is no harm in that.