I am trying to index several texts into solr, so I am a little confused about indexing them. I have tried to use the /update request handler instead of post tool. When I am using the /update does it re-index a document? Is it proper to upload my data to solr-cloud, with this particular handler?
There is no difference between indexing and reindexing a document. Reindexing just means that you're re-submitting a document that is already present in the index; the implementation and how you do that is exactly the same. The only difference is that the existing document is marked as deleted in the index before the new one is indexed.
And yes, using the /update endpoint is usually what you want to do.