Firstly, welcome to SKF.
The minnows and rummy might take an opportunity to nibble at the shrimp, but the amano won't so no need to worry about the amano at least.
These questions are a bit more difficult to answer, as it is based on circumstances.
As a general indication, any shrimp at 1cm or larger should be ok.
It could take 3-4 months to get to that size.
It's also difficult to predict is your minnows and rummys will leave the shrimp alone even if they are more than 1cm long. Some people have fish that never bother their shrimp. Some have fish that are real shrimp hunters.
There is no guarantee that even a shrimp larger than 1cm will be safe. Fish don't swallow shrimp whole, unless it is a little shrimplet. They nibble at the legs and antenna of the shrimp until the shrimp dies. The betta is almost certainly a risk. Tetras can be a risk, and Rummys are certainly right up there, being big and bold.
It can be done, but there are risks.
Provide lots of hiding spots the fish can't get into. Provide lots of plants. Keep the fish regularly fed. That should help minimise some of the risks.