Yes, that will work - obviously you connect to the "coil" pins. Note that that is a 2-coil latching relay: activating one coil will switch the contacts one way, activating the other will switch it back.
Datasheet (found by inspecting the part number with zoom on that page)
No you should not do this. Sometimes it is explicitly allowed on the data sheet (but not that I can see on this data sheet), and when it is, in my experience you never get as much as double the capacity.
Paralleling physically separate relays is worse again because they're not physically moving together- expect welded contacts etc. if you tried that.
If you can split the load (for example, instead of a 40A heater use two 20A heaters) then you can get an equivalent functionality.
You could think about ballasting the loads (wasting power to roughly equalize the currents) and fusing each contact separately, but I don't think that's a good idea at all.
Note that using the relay at the maximum rated current will lead to a pretty short life (only 100,000 operations for a resistive load), which might be only weeks or months if it's switching continuously. At 3HP (motor load), the life is only 1,000 operations, so at once per minute it won't last a single day.
Edit: With the added information that you're using the relay to switch effectively at a relatively low DC voltage and you're mostly concerned about carrying current.. I can't say categorically this is really a horrible idea with a single relay, but I think I'd get on the horn to the manufacturer and see if it's possible to get any buy-in. It comes down to variability in contact resistance vs. the resistance of the connections (plus whatever, hopefully balanced, resistance you add externally). When one of the contacts inevitably fails first, I think I would prefer the relay to not emit excessive amounts of smoke or flames). I think you're okay at 40A (with AgCdO contacts) given the UL508 rating, but beyond that is in question.
If you really need such a high carrying current, the Omron G7Z appears to explicitly allow paralleling the 40A contacts without derating, for 160A total capacity, but perhaps not with the blessing of safety agencies.
Best Answer
No, that's the maximum current. The coil resistance is 180 Ohms at 5 V -> 28 mA.
Edit: And if you want to switch at 3 V, find a different relay. This one isn't specified at other than 5 and 12 V.