How to alter views query for a Search API index view

Use hook_search_api_views_query_alter() instead. See includes/query.inc in the Search API Views module for the definition of the views query class. $query->getSearchApiQuery() gives you the Search API query object. See includes/query.inc in the Search API module to see what you can do with that.

Here is the output of dpm ($query->getSearchApiQuery());

 ... (Object) SearchApiViewsQuery
    group_operator (String, 3 characters ) AND
    pager (NULL)
    view (NULL)
    display (NULL)
    plugin_type (String, 5 characters ) query
    plugin_name (String, 22 characters ) search_api_views_query
    options (Array, 3 elements)
    definition (Array, 10 elements)
    is_plugin (Boolean) TRUE
    base_table (String, 35 characters ) search_api_index_default_node_index
    base_field (String, 13 characters ) search_api_id
    where (Array, 1 element) 

First off, this looks much more like dpm($query); If it is really dpm ($query->getSearchApiQuery());, then there is a weird bug there.

Second: What do you want to say with this? Is it good, bad, do you want help or do you want to help?

It is kind of you to correct something wrong if it is not true.

I just posted it for someone who might have an interest in the value of $query->getSearchApiQuery().

How can we do groupby here like $query->add_groupby('nid'); in hook_vews_query_alter() ?

How can we do groupby here like $query->add_groupby('nid'); in hook_vews_query_alter() ?

It's possible to do something similar by using the Search API Grouping module (though that works globally on all searches for the index) with Solr. (Or by using the same query options manually.)
Other than that, grouping isn't supported by the Search API.