No. A homonym doesn't use "like" or "as", that is a simile. A homonym is a word that is spelled the same as another word but may have a different meaning. For example "tear" (like when you cry) and "tear" (to rip).
his favorite hobby is fishing
Fishing is a recreational activity, which would make it more an interest than a sports hobby.
Fishing
Jellyy fishing
bass fishing
fishing fetch (for dogs)
Yes and if you like it enough it can become an obsession/lifestyle.
Fishing, swimming, running.. etc..
Hunting Fishing Cooking meat
Dennis's favorite hobby is fishing.
Hurst Hugh Shoemaker has written: 'Science-hobby book of fishing' -- subject(s): Fishes, Fishing, Juvenile literature
Yes he does a lot of fishing in his spare time