Looking at a unit is there anyway to tell if it has moved or not in the current turn? I've noticed the emblem for the unit greys out, but it also seems to remained greys out if the unit has been fortified.
How do I tell all the possible tiles a unit can move too? I've noticed that when I click to move a unit a blue outline is briefly shown, but I want to see this before I issue the move command.
You can see whether a unit can still move from the unit list - you can open the unit list screen by clicking on the symbol and the top-left corner and selecting the 3rd option. Each unit has a colored circle next to it, as well as text explaining what it is currently doing (e.g. fortified). If there's no text, it means the unit is awaiting orders.
So in short, any unit you see with a green or yellow circle can still move this round, even if it's not awaiting orders - you can click it directly in that unit list screen to select it, or even double-click it to select it and center your view on it.
To see all the available tiles a unit can move to, either click the move-to button and then select a tile, or hold the right mouse button (don't just click it!). Then, when you release it, the unit will move to the designated spot. In both cases, you will have a blue outline showing the limit of where the unit can reach in the current turn.
If you use either of these methods and then designate a location beyond your movement range, you can even see the entire planned route (well, at least the first 8 turns of it or so), how many turns it will take to get there, and what position the unit will be in at the end of each turn.
I see you mentioned the unit emblem turning grey-ish. This only happens when a unit has no more movement points remaining in that turn. A unit may be busy doing something (e.g. fortified or constructing something) so it's not awaiting orders, but still with moves remaining, so it will still have a non-grey emblem.
