ghost shrimp/betta

yes

invertebrates are extremely sensitive to water quality. so if there is even a touch of ammonia or nitrite in your tank, or a high amount of nitrate, they will die. you might want to change the water every other day. but that's just me.

also there's the chance that your betta may try to eat it. but ghost shrimp are cheap. i'm personally going to use ghosties as "testers" with my betta before i try any more expensive shrimps (Amanos, red cherries).

1 gallon is way too small, even for a betta. adding the shrimp would just be addtional bio-load your betta does not need to experience especially with only the weekly water changes being done. something that small needs at least 2 water changes a week. the amount of waste your betta makes will accumulate much more quickly. if you want your betta to thrive, be healthy, and have space for roomies, you may want to opt for a 5 gallon tank with a heater and a small sponge filter. at that point, you may add 3-4 ghost shrimps/snails but its different will all bettas. some will ignore the shrimps/snails alltogether, while others see it as a tasty snack.

My Betta lives in a 5 gallon with 5 ghost shrimp that he doesn't even look at. He has however virtually eliminated all the snails I have in there. Yum Yum.