Link to Global Fields like you can with the entries fieldtype
Not directly. You could have a dropdown of all the global set handles (use Dynamic Fields Plugin if you don't want to maintain this dropdown manually), and then in your template fetch the global set from its handle with getSetByHandle:

{% set globalSet = craft.globals.getSetByHandle(entry.globalSetHandle.value) %}
{% if globalSet %} {# could conceivably be null #}
  ... {{ globalSet.someField }} ...
{% endif %}