well since there are questions and no answers yet, I'll jump in... I don't use the term "writing" to refer to an icon unless I am talking to someone who makes a point of using that term and I don't want to offend them. The same verb in greek can refer to writing and painting. Since I use paints and a paint brush, I say that I paint icons. Some people like to say that icons are like scriptures in pictures and as such they find the word "write" to be more appropriate. I don't think it matters either way, I just get a little irked when people insist that we must say "write."
Icons are more than mere decorations, and shouldn't really be treated as a painting or a picture to hang on a wall. Icons are a visual proclamation that the God who created the world became a man for our salvation, that he suffered and died for us, that he rose from the dead, and ascended into heaven taking our human nature with Him. Furthermore they testify to the fact that Christians can be transformed back to the image and likeness of God, and that indeed God dwells within Christians and shines forth in those who live according to His will. They proclaim the same message that the Gospels do. Hanging an icon in your home or your church makes a profound statement. While icons can be decorative, they are not decorations. A Bible can be beautifully printed, bound with the finest materials, and filled with beautiful word, but it would be a mistake to see it as a work of art rather than as a means of encountering God.
With that being said, I don't see a problem with giving icons to non-Orthodox people. It may draw them to Orthodoxy after all, but I would make sure that the person understands that it is not just a picture to you and that it should be treated with a certain degree of respect. Just as we would not toss the Bible on the floor or use it as a coaster on the table, an icon should be used as a reminder of what it represents. If your friend will not do that, I think it would be better to get them some other piece of art.
I think that addresses all the questions except for materials. I don't know that there are really wrong materials for painting an icon (although there very well might be some exceptions depending on intent) but there are some that are more suitable than others. The one in particular that stands out as a poor choice for iconography is oil paints. Oil paints, due to their very long drying time are more suited to paintings with lots of blending, and not so much to the layered style of more traditional iconography. That being said, I know of an iconographer that works in oils and creates traditional looking icons. I just can't imagine how long he must wait for things to dry. Some people will say that egg tempera is the only correct medium for icons, but I disagree very strongly with such a statement. Icons have traditionally been done in encaustic (a method of painting with melted wax and pigments), fresco (painting in wet plaster), egg tempera, acrylic paints (in the years since acrylic polymers have been created), and of course mosaic. I'm sure there are many other materials that have been used over the centuries, and many more that could be used.