What is ankle reconstruction surgery like?

Need specifics. Depends on what exactly is being done. Various procedures around the ankle joint ranging from fixing ankle fractures to correcting deformities and treating arthritic or degenerative conditions when appropriately indicated have a great potential to improve the symptoms and worthwhile.
Depends. Ankle reconstruction can mean many things ranging from ligament reconstruction to ankle replacement to bony realignment. If you mean ligament reconstruction, this involves either tightening existing ligaments or using tendon grafts to replace deficient ligaments.