Do all veins carry oxygen-rich blood?
Actually, almost all veins carry deoxygenated blood back to the heart. I say almost because if we talk about fetal circulation, the exception applies.
In fetal circulation, the umbilical vein carries oxygenated blood from the placenta to the fetal heart. The deoxygenated blood that returns, returns via the umbilical artery and the cycle repeats itself.
No. Excepting the pulmonary veins, all veins carry de-oxygenated blood.
In the body, arteries generally carry oxygenated blood and veins carry de-oxygenated blood.
The exceptions are the pulmonary arteries (which branch from the pulmonary trunk artery) that transport de-oxygenated blood from the right ventricle to the lungs for oxygenation, and the pulmonary veins that transport oxygenated blood from the lungs to the left atrium or auricle.