There are many types of operations developed to correct these types of problems. Fusing one of the thumb joints to a more functional position. Surgery may be helpful to correct deformities caused by rheumatoid, but may also be recommended to prevent problems before they occur - such as tendon rupture. It really depends on what the problem is, but in general, carefully planned surgery is worthwhile. Surgery is most helpful for correction of deformity and for preventing tendon rupture.
Surgery is less likely to help improve the strength of the hand.
This really can't be predicted. Simple surgery to prevent tendon rupture can help avoid complications which would require more extensive surgery to correct. Surgery to correct nerve problems such as carpal tunnel syndrome may prevent progressive nerve damage. Other than that, it is a quality of life choice. Some people have deformities which develop over a short period of time, and then don't get much worse.