Core Lightning v0.11.1 what's the house icon for, doesn't have a desktop icon next to it,can I still use this for the desktop
It is not a house icon for this one, it is ">_" and it means that the wallet is CLI only. That means yes you can use it on a desktop, but it has not GUI.
Zeus v0.6.0-rc3 - what's the house icon for, doesn't have a desktop icon next to it, can I still use this for the desktop
Zeus is a mobile interface to LND, CLN and Eclair. I think the house icon is for the "remote backend". No desktop as this is a mobile only wallet.
If you can't run a full node for some reason, I'd suggest you try Electrum for Desktop.
Robostats is not a active site compared to agora.
I can't say for certain because I don't use them, but generally the liquidity is low on all these services. It is simply too inconvenient in many ways, which pushes many of those who would use them into alternative solutions such as no KYC swap sites. Of course each thing comes with its own set of risks, pros and cons. For example no matter what you do on Robosats you won't get a sudden KYC request, but you are liquidity limited and it requires more setup. On more centralized solutions, there is a risk of a sudden KYC request but the liquidity is great and no setup is needed. Pick the disadvantages that you prefer and deal with it.