The first item has no dots as it is only a one tier item. It is a "starter" item. One that you would usually get at the start of a game to get good low cost stat boost, but sold in end game for a better item.
The second item is flashing because you have enough gold to purchase the next tier up (note this doesn't always mean the item you are building to. just that you enough enough for one of the branches)
The third item is complete, 3 dots means its a tier 3 (max level) item and comes has a sufficiently stronger passive ability.
If the passive only activates after a cooldown (ex. magi's blessing). the item will be greyed out with the cooldown timer (the other stat boosts from the item itself will still be active)
You can free your mouse ingame with Left Alt (default) to mouse over the items and view the stats it gives and other information, but to view the item tree you need to open up the shop with i (default).