Can an eye infected with keratoconus burst somehow?

Not an infection. Keratoconus is not an infection, but a hereditary degeneration of the cornea, which causes the cornea to thin out and become warped (irregular astigmatism). Rarely, it can become so thin that minor trauma can cause it to rupture.
No. Keratoconus is a problem with the structural integrity of the cornea (the window at the front of the eye). It is not an infection. Keratoconus can break down if extreme and could actually erode through if it gets infected. This is very rare however. Since keratoconus is slow in evolution, you should by now be looked at by a corneal specialist who can help you through this.
No. While eyes with keratoconus can become thin, I have never heard of one bursting or rupturing spontaneously. Of course - with trauma - there is a risk.