does it just stop new hair from growing?

It just stops new hair from growing.

would Finasteride (and avodart) also be effective in stopping new hair growth? (while being safe for males) It is "...a type II 5alpha reductase inhibitor. [It] blocks the conversion of testosterone to dihydrotestosterone (DHT), a potent stimulator of hair loss in scalp follicles and hair growth in body hair follicles that have androgen receptors."

I believe products that stop hair loss can cause growth on other areas since they're stimulating hair.

No, actually. Drugs like Propecia and Avodart work by reducing the actions of DHT at the hair follicle. While DHT is what causes hair on the HEAD to fall out, it also is what causes body hair to grow. So, taking something like Propecia will stop balding, but should also reduce body hair as well. I used to take it, and it's commonly prescribed to other transsexual people as well for its anti-androgen effects.