Yes, you can use Lunette since it doesn't contain latex. Lunette is made of medical-grade silicone which doesn’t cause allergies. There are many types of silicone, but the silicone used in the Lunette menstrual cups has been tested to be safe. The Lunette is made of the best possible quality of silicone, the same kind which is used in heart valve devices and artificial joints.
Even if you have long nails, you should still be able to use the Lunette menstrual cup without any problem. The first time you use the cup, you have to learn the best way to insert and remove it without scratching yourself. Inserting and removing the cup should not be harder than doing other things with long nails. However, note that with long nails, you have to pay particular attention to hygiene. Fingernail beds are breading grounds for bacteria, so make sure to wash your hands and nail beds carefully before handling the menstrual cup.
According to the Finnish AIDS Council, you can flush infected blood down the toilet. The virus becomes ineffective when mixed with excessive amounts of water. If you need to empty the cup somewhere there are no toilets (e.g. when camping), make sure to cover the blood with some soil, preventing anyone else to come in contact with it. Only fresh blood transmits the virus, so when exposed to air, the virus will die.
You can use your Lunette cup with an IUD or with a contraceptive ring. It may be helpful to discuss using them together with your doctor. The strings of the IUD should be cut as short as possible and you should monitor their length regularly during periods. If the strings seem longer than normal, it might be a sign that the IUD has moved.
A study made in Canada tells that the overall rate of IUD expulsion within 2 months of insertion was low (3.5%), and was statistically no higher for women who used tampons or menstrual cups than it was for their counterparts who used pads. Read more here.