RM pro mini newbie here.
1) With IHC app. it appears there is not a way to turn on both the TV & Cable Box with one command, like Alexia turn TV on ?
Yes you can, here's how I do it.
1:Create both devices in IHC
2:In your Alexa app create a group and add the TV and Cable box
3: for the group name give it something which Alexa can't confuse with something else.
if you used TV as the TV device name in IHC you can't use TV for the group name.
I use "NEWS" since that is what I basically use it for.
2) Can I use a combination of IHC and the RM tasker app ?
Does this RM tasker app contain logic to prevent it from sleeping ? If not, any recommendations. It is running on a Galaxy tab, android 6.
Yes you can, though I only used it (trial) briefly.
I believe the tasker app needs the Broadlink e-control app to work
If I remember you needed to set tasker up as a server.
As for sleeping I believe that is an Android system setting I never had issue with it seeping on my Galaxy S
I currently use the RM Bridge running on my GalaxyS and have no issues when the phone screen shuts off.