What ligament goes across the talus bone? How does it heal once injured? Is an injury to that ligament a serious one whe it causes pain to walk/stand?

Many. There are several ligaments that attach to the talus-anterior talofibular and posterior talofibular laterally (outside of ankle). Calcaneofibular ligament spans the talus. Medially the deltoid ligament. Most ankle ligaments heal when torn (sprain). This can take several months. If pain persists see your primary care doctor or orthopaedic foot and ankle specialist.
Yes, serious injury. The talus bone (second largest in foot) is the bone next to the calcaneus (largest, the heel) and this area is where the most weight is centered each step you make, any weight-bearing. Any injury to the ligaments (the strong band that attaches bone to bone, muscle to bone) will cause pain, and if continue weight-bearing on it when painful, it will not heal and get worse. Rest it, pt, ortho.