It depends on your CDM version. On version CDM 5.3 and 5.4 death table is used to store all the death related data, so use it. On version 6.0 death table is removed and fields to person table added, so you have to use them. Check the specifications on different versions here.
However, you can still map death to condition/observation ‘death’ and use these tables instead of specific one, but this approach is strongly not recommended.
Patient transfer to intensive care unit - use visit tables
Stabilized - I think, the better shot would be Observation (observation_concept_id - patient status, value_as_concept_id - stabilized) or even Condition, but not a standalone Observation with concept class id of Qualifier value
Signposting to rapid response team - great as a procedure
That’s only one of the possible approaches to use, yours would be fine too in analytical perspectives, but it’s not canonical and if you would ever want to collaborate with other researchers, you won’t be able to, until they have the same data structure. Also, your mapping will determine tables where to put records.
Good luck with this!