When preparing food for the flies, it is easy to make it too hard or too soft. This is an advantage of the Sussex media mentioned in Fruit fly food which is right every time. Too wet media can be countered by inserting twisted or screwed kitchen roll or newspaper - both absorbing some moisture and creating walkways for the flies. This can be done in any case, and can increase fly yields if there is often a shortage of pupation sites.
Mold is scarcely a problem if mold inhibitors are used, but also moldy cultures are usually lightly populated. The flies (and larvae) prevent mold when present in great enough numbers. Using narrow vials with a small surface area certainly helps. When reusing old vials ensure they are cleaned efficiently - failure to do so will also increase the likelihood of mold. A soak in weak bleach can help, but make sure they are rinsed thoroughly afterwards.
Can destroy a culture. Some merely feed on the media with the flies, but some are parasitic or egg eating. Mites can be treated with Benzyl benzoate soaked bungs, but it is probably easier to discard all cultures and get clean fly stocks. Mite prevention is probably more appropriate, and flies should be housed away from possible contamination, such as in a larger closeable cabinet.
This does happen. Flies can breed with wild flies through thin vial tops (netting for example), or mix with them during handling. Where possible use foam bungs, and try to keep your flies in a closed space away from potential contamination. Once this happens, you really need to replace your stocks and start again.
Yes they will get out. I use a vinegar trap; vial of vinegar with a perforated tin foil lid. The flies head straight for it.