Not seeing an index you created on the indexer on other systems (DS, SH) is expected and normal. Neither search head nor deployment server are supposed to have indexes, that's what indexers are for.
If searching for that index doesn't return events then there are several options:
Is the indexer getting data? Since you've seem to have the UI on the indexer still enabled, see Settings -> Indexes to check if that index shows >0 events
Is the SH connected to the indexer? Check on the SH, Settings -> Distributed Search -> Search Peers
Is your user authorized to search the index? Usually fine if you're using the default roles
Are you searching the index? Make sure your search is index=that_index
Are you searching a time range matching your data? When in doubt, use All Time until you found something
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