Nitrites will definitely kill fish and ghost shrimp. So will the chlorinated water from most taps if that is used without treatment Steve mentions. So - very frequent water changes, or a filter is needed. Tom's right, if you just want to change the water every few days - no need for filter (because the ammonia, then nitrite will start to build up in just a few days). But if you want ghost shrimp or fish to survive you will have to be sure to remove the chlorine or chloramine if you have municipal water for your water changes. Most municipal water supplies tend to go with chloramine now as it is much more stable in the water than chlorine - so just letting the water sit a day or so isn't as effective with chloramine. SO adding treatment as the choices Steve mentions are necessary. Doesn't matter to the turtle, though - they will do fine with chlorinated water. Turtles will also do OK with the ammonia and nitrites that a tank will go through, but I personally believe from my experiences, if left unchecked, it can lead to some skin / shell issues at least with some types of turtles. So if a long term setup - I definitely prefer to establish a filter.
If you do have a filter, it does need to get established and will go through a new tank cycle. The waste in a tank turns to ammonia, which will then be converted to Nitrite by beneficial bacteria as the bacteria starts to get established. The nitrite will then get converted to nitrate which is harmless except in really large concentrations. My tap water comes out with high levels of nitrate already - as is the case with many water supplies including most wells. Plants consume nitrate so many will keep plants in their tanks and ponds to help keep that more in check, as nitrate is plant fertilizer! IN a natural environment - that is the balanced cycle.
A filter will take 4 - 6 weeks to get established, but you can speed that by adding bacteria. With just your turtle and ghost shrimp I wouldn't worry about that too much. Just give it time before you expect the ghost shrimp to do well long term (If they survive the turtle!) It just will be important to use treated water for your water changes, and don't forget to only use treated water to clean your filter media - or you will be killing off the bacteria and have to start all over again.
Sorry I got so wordy, but no sure how to answer the question of cycling and nitrites / nitrates being harmful to ghost shimp vs turtles without a little explanation.
If you do have a filter, it does need to get established and will go through a new tank cycle. The waste in a tank turns to ammonia, which will then be converted to Nitrite by beneficial bacteria as the bacteria starts to get established. The nitrite will then get converted to nitrate which is harmless except in really large concentrations. My tap water comes out with high levels of nitrate already - as is the case with many water supplies including most wells. Plants consume nitrate so many will keep plants in their tanks and ponds to help keep that more in check, as nitrate is plant fertilizer! IN a natural environment - that is the balanced cycle.
A filter will take 4 - 6 weeks to get established, but you can speed that by adding bacteria. With just your turtle and ghost shrimp I wouldn't worry about that too much. Just give it time before you expect the ghost shrimp to do well long term (If they survive the turtle!) It just will be important to use treated water for your water changes, and don't forget to only use treated water to clean your filter media - or you will be killing off the bacteria and have to start all over again.
Sorry I got so wordy, but no sure how to answer the question of cycling and nitrites / nitrates being harmful to ghost shimp vs turtles without a little explanation.