I don't have experience with International Packing and Moving services, but I did recently have a (somewhat) direct experience with Packing and Moving within India. Though not directly applicable, I can answer your questions in that context.
1. My cousin used the services of Agarwal Packers & Movers about a month back to move some stuff over about 300kms within India. The service was simply outstanding. (More about it in the next few answers).
2. Yes, it was end-to-end. Nearly all household articles (kitchen utensils, appliances, dishware, cutlery, curtains, books, shoes, clothes, framed photos, TV, refrigerator, washing machine, a couple of almirahs, 2 couches, 4-5 chairs, two small tables, a mattress and a cot) used by a person staying alone needed to be moved. All this was on the 1st floor of a building with pretty narrow stairs (3-ft wide).
3. Yes, insurance was optional and we opted for it. It was charged at 3% of the total of the declared value of the articles. We were free to declare any value we liked.
4. The way the articles were packed was outstanding. In the case of the electrical appliances, we were only expected to unplug all wires and hoses from the electrical/plumbing outlets. The packers arrived with about 8-10 people and all the packing supplies they needed. The everything, including the electrical equipment, was packed very carefully, securely and efficiently. They used a lot more packing buffer that I would have, if I had to do the packing myself (and I'm one paranoid android). After all the packing the equipment was wrapped in many layers of cling-film and labelled with handling markings. None of the items had original packing, but that was not an issue at all. Once packed, the items were taken down very carefully and loaded onto their truck carefully. The other stuff went into cartons, and each carton was labelled with information about the contents (books/clothes/cutlery etc)
They took just 5 hours to pack everything and load everything.
The items were unloaded the next day at the destination as carefully, and they even unpacked the stuff for us. Nothing (except a couple of glasses and a serving tray) broke or got damaged, thankfully.
5. Customs was not an issue, of course, but the items were moved across a state border. We had to give a declaration in a letter (with photocopy of ID proof) stating that all items were items of personal use, had been in personal use and were not intended for sale.
6. It was a bit costly. It cost my cousin Rs.35K total. Other than the big items of furniture and the electrical items, there were 20 cartons of about 24"x24"x24". They charge by number of items and the distance to be covered. But frankly, considering the service and the speed with which it all got done, she was pretty satisfied. If we had to organize all this, it would have taken us 2 days to pack it all (and not half as efficiently as they did) and also a lot of hassle and headache to have the stuff loaded, moved and unloaded. Doing it ourselves might had cost about 25K-28K probably.