My son was born with bilateral congenital cataracts in both eyes but were remove. Can he see well at 1 year?

Depends. The level of vision your son is capable of will depend on the severity of the cataracts and the age at which they were removed. You should consult an eye doctor specializing in pediatrics in order to monitor his vision.
Depends. On when cataracts were removed, amount of amblyopia, were intraocular lens placed/any residual refractive error, other ocular comorbidities such as glaucoma, success of the surgery, etc.
Not sure. Rapid diagnosis and treatment of congenital eye problems usually, hopefully avoid long term issues. Unfortunately, i cannot tell you for sure whether he has goo vision or not without examining him, of course, proper follow-up, examination & likely glasses/spectacle correction should be done.