On collection page, fetch all the collections. If your current collection handle is t-shirt and your sub collection handle is linen-t-shirt. Check for all the collections which contains current collection handle, then show the details.

{% assign currentCol = collection.handle %}
    {% for collection in collections %}
      {% if collection.handle contains currentCol %}
         {{ collection.title }}
         // further code 
      {% endif %}
    {% endfor %}

To access specific collection attributes, you must know collection handle and use this kind of code :

{{ collections['the-handle'].url }}

So to achieve what you want to do, here is what you could do:

{% assign collection_handle = 'the-handle-of-collection-you-want' %}
{% for product in collections[collection_handle].products %}
    Do your stuff
{% endfor %}

Note that you cannot access a collection through its title. Only handle.

Learning more about what's handle: https://help.shopify.com/themes/liquid/basics/handle

HTH

You have access to the current_tags, refer to docs: https://shopify.dev/docs/themes/liquid/reference/objects/current-tags

This will return an array of all the tags you are viewing at the moment (in case you are viewing more than one tag).

So your check will be:

{% if current_tags contains 'mens' %}
    do something
{% endif %}

That's pretty much the just of it.