Many thanks for your questions.
Not all women get heavier periods once it is fitted, but many do. Periods tend to be worse in the first 3-6 months and better after that. The general pattern with the copper coil is that women experience spotting before their period and then the normal period which is slightly heavier and then spotting at the end. Because of the spotting before and after each period many women find that they bleed for more days per month than without a coil. If your periods are already heavy then you may wish to consider a hormonal coil ( see below). If your periods are currently light then you may find the slight increase in bleeding associated with the coil acceptable.
You could consider a hormone coil, this tends to make your periods lighter and many women stop bleeding all together on the hormone coil. Like the copper coil it can cause irregular bleeding in the first 6 months which then gets lighter and lighter so that many women (about 80%), but not all, have very little or no bleeding at all by the end of the first year.
Your question about fibroids is important and the answer depends on where the fibroid is. As you probably know, a fibroid is an enlargement of the muscle of the womb. It is not dangerous, although it can sometimes cause heavy bleeding. If the fibroid changes the shape of the womb like in the picture below then it may be difficult to fit a coil. You could have an ultrasound scan before your coil is fitted so that you can see where the fibroid is. If it is on the outside of the womb then it will not disrupt the coil at all.
Finally, the strings only hang down into the very top of the vagina, like this. In fact they do tuck round the cervix. They are about 2cm long and feel like thin nylon string, like fishing line.
This is quite a lot of information to provide in one post so do come back to me if anything is not clear.