gerundial infinitives or simple infinitives

[Babai]

1.Go fishing 2.go swimming.3.go hunting 4.he came here checking out the room here fishing,swimming,hunting,checking are gerundial infinitives? can i write these sentences using simple infinitives like 1.go to fish 2.go to swim 3.go to hunt 4.he came here to check the room. please explain these grammatically. Thank you.

[charliedeut]

1. Go fishing 2. Go swimming. 3.Go hunting. 4. He came here checking out the room.
Here 'fishing', 'swimming', 'hunting', 'checking' are gerundial infinitives? Can I write these sentences using simple infinitives like 1. Go to fish. 2. Go to swim. 3. Go to hunt. 4. He came here to check the room? Please sir [some of the people likely to answer are female members] explain these grammatically. Thank you.

charliedeut