1. Example:

OnlineMapsMarker marker = OnlineMaps.instance.AddMarker(lng, lat);
marker.tags.Add("mytag");

2. OnlineMapsMarkerBase.enabled.
Example:

OnlineMapsMarker marker = OnlineMaps.instance.AddMarker(lng, lat);
marker.enabled = false;

3. If you want to remove the markers that have the specified tag, use OnlineMaps.RemoveMarkersByTag.
You have direct access to the array of markers, so you can implement the rule of removing markers of any complexity.

1) How can I assign a tag to a marker (probably we should somehow do it during its creation via OnlineMaps.AddMarker)?
2) Is there a way to "disable" and "enable" 2D markers? Or we should remove/create them instead?
3)How can I pass the markers (which I can select using the LINQ example) to the OnlineMaps.RemoveMarker() function in order to remove them?

Thank you!

You can use OnlineMapsMarkerBase.tags or OnlineMapsMarkerBase.customData to store the group ID (or other information that you need to define a marker group).
You have direct access to the array of markers, so you can easily make a selection, for example (LINQ):

foreach (OnlineMapsMarker marker in OnlineMaps.instance.markers.Where(m => m.tags.Contains("mytag")))
{
    // do something
}

or

string groupID = "mygroup";
var markers = OnlineMaps.instance.markers.Where(delegate(OnlineMapsMarker marker)
{
    // It does not matter what CData class is here. 
    // You can store any object in customData.
    CData data = marker.customData as CData;
    return data != null && data.group == groupID;
});
foreach (OnlineMapsMarker marker in markers)
{
    // do something
}

Is there a way to display/hide/modify(change color) of a certain group of 2D markers and not all of them?

Is it possible to do this with 2D markers created through the inspector, or in this case markers should be created through the code?

I think as an option I could create the markers via the script and add a specific tag to them in order to manipulate them later.
Is there another way designed for Online Maps?

Thank you!