First of: Welcome to the Forum!
Very good move to test the water first and post this here, a lot of times that's reasoning for issues right there is nitrate peaks etc, but in your case we can rule this out.
There could be a number of reasons for the shrimp. First of shrimp generally seem to have troubles in new tanks and die quick in tanks that are not established (established meaning fully cycled and running with the fish for a number of months). Also a possibility: Have you used any type of fertilizer in there of any kind; they react deadly to Copper in ferts? Last but not least, what type of filter are you using depending on the size they were when you got them they could have litterly went down the drain?
Now both of your exiting fish may look sweet & innocent to you, but they will feed on the shrimp well, so this could very well be the case, despite what the Salesman promised you, I'm sorry to say that.
What I would do in your case: Heavily plant the tank once the plants are beginning to establish themselves and start growing, then try to have shrimp again (so they have better chances of hiding/ running away from their predictors).
For a well planted tank, you do not need a CO2 system, this is definitely not a must have for having plants.
My own tanks are all set w/out CO2 nor fertilizers nor nothing but GOOD light and good water. IMO a good light is the biggest key to healthy plants. So save yourself the $ for the machinery and spent the $ on a TON of plants and a proper light (What lights do you currently have on there?)
Also I'm sure Byron will check in here later and tell you all about the lights and the non-necessity of CO2