In the compass at the bottom of the screen there are icons for quests you need to do.

Is there any way to tell which icon represents which quest?

Can't put the cursor on them. I notice the box at the top of the icon is sometimes blank and sometimes filled in.

Sometimes more than one is filled in.

I'm wondering how to tell which one is my current quest.

The compass icons only show up for quests you're tracking, so untrack the quests you're not doing.

You can go to the quest screen on your pip boy and toggle those missions on and off, which will light up or remove the compass pip for that mission.

None filled in box is actually the custom marker you can place, not quest related, and actually you can see what quest objective the marker points too, just hover over it on ya map.

I'm not sure if this is what you are asking, but you can press the show on map button (Square on PS4) to see where each quest is supposed to take place at.

Also, if a quest marker looks like a little door, then you actually will be led to a door or zone-point which you have to enter. What is vexing is when the point you need to reach is, like, up high in a skyscraqer, but "outside" the skyscraqer.... the pathfinding then can be complicated, involving entering ~nearby~ buildings and going up to higher floors, crossing rooftops, then going down buildings to a lower level, crossing over to another building, and so on. Aren't many of them, but those kind of situations make me tempted to try VANS and see if it would make things any faster.

How do you do VANS? How do you start it?

Click and hold the VATS button, even if there is no enemy nearby you enter VATS mode.