Yes, now with advancement in orthodontics (braces)Teeth can be aligned at any age, provided the gums and underlying bone are in good health.No it does not cause any problem after alignment,in fact it increases the life of your teeth as it eliminates food lodgement, cleaning becomes easy,bite becomes better.Cost Varies depending upon the case,which determines the time and what type of braces you want(metal,ceramic,invisible) and various other factors.
Next Steps
Consult an Orthodontist(Braces specialist)
to know in detail about your problem,possible solutions,time required,cost etc.