Lack of embeded fonts, wrong color space, embedded profiles that do not match workflow output profiles, bad fonts, cmyk or rgb type-not black, low res graphics embedded into pdf, files with "borrowed" copyrighted materials and no credit line, files sent in printer spreads, wrong size-not at final output size, no bleed.
Native Application Files:
No links to the high res graphics, no fonts, bad fonts, version of software from 1995 that does not support what they are trying to do, no bleeds, files built in spreads, software the printer does not have to output the job.
2. Always call and talk with a person in prepress, not the sales person>
Let them listen to what you want and tell you what they need, then you will get what you expect.
3. Options range depends upon your printer. Most shops do not support film based proofs - such as Chromalin or MatchPrint any longer due to the cost and lack of product. Proofs depend upon customer demands and so InkJet proofs pulled to match presss room specs are common place. Some shops use toner based proofs also from digital presses or higher end print egines such as copiers. Some shops still pull press proofs if you are willing to pay for them. Cost depends upon alot of things, size of the job, proof type selected, relationship with vendor, etc...
4. Proof sign off should happen both internally at the printer and externally at the customer. Internally, the person that pulls the proof should reviiew it for content againest the file supplied and typically will pass to a CSR or the Sales person to review againest the specs of the job and then pass to the customer for sign off for color and content and dieline (if this applies).
Keep in mind that depending upon the size of the shop you deal with and the scale of the project all things change. If you go to the local mom and pop shop that has 3 people working it, the person that pulls the proof will more than likely be the person that prints the job.
Hope this at least gets you started, others will weigh in with more.