Homeopathic treatment definitely has a cure for warts. Although, warts in bunch can be cured easily, solitary warts are slightly stubborn but can be cured after a prolonged treatment. But there is a permanent cure. Your first query is solved.
Secondly, surgery removal is recommended because there is no medicine to dissolve the warts or remove them permanently. Surgery is nothing but cauterization or laser treatment which does not provide permanent cure. The warts have a chance of recurrence even after the treatment.
Next Steps
Advice you to visit an experienced homeopath nearby and get yourself checked.
Health Tips
1. Don't irritate the warts.
2. Try not to apply anything externally. It doesn't have any significance.