1. Doing good to others is the best way to be happy.
2. Doing evil to others is terrible.
3. Cut out/completely all the pieces.
4. Cut all the pieces out/completely.
(Can we use 'completely' instead of 'out'? Are all the expressions grammatical?)
5. Tape a stick to/on the back of the puppet's body.
(Which preposition do I have to use, 'to' or 'on'? Are both OK?)
6. Join the arms to/on/at the shoulders. (Which prepositions are proper?)
#3 and #4 - delete "/completely" -- it is not interchangeable with "out"
#5 -- either preposition will do; I think "to" is better.
#6 -- use "at"