In fact, i wanted to play the Space Race which Steve used to play in earlier version.  But i think he was  playing the 4 differents countries. . .

So no way to have a multiple nation earth with space race. . .

You have to leave Spacemaster mode on and play each race.  The AI is, unfortunately, not designed to work this way.

I don't think there is a way to do what you want without the designer password.

even if there was, NPRs are not designed to operate this way, and will inevitably begin a cataclysmic war within weeks.

"I'd like to give an alien empire trade (or higher) access to my empire, so that they'll like me more rapidly, but the radio button is greyed out.  What's going on"
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Unfortunately, you are not the all-powerful leader of your vast empire - public opinion matters too.  If you look on the Diplomacy (ctrl-F5, aka "Intelligence and Foreign Relations") screen, you'll see a "Current Diplomatic Rating for this Race" number.  This is how much your population likes the other race - positive numbers corresponding to "favorable".  This has to be above the threshold for each diplomacy state before the button for that state will unlock.  For trade access, this threshold is 100; for others it's higher.  If this number drops far enough into the negative (due to you detecting their ships on active sensors in your populated systems without appropriate treaty status, for example), then they'll automatically be reclassified as hostile.

"I just encountered an alien spaceship!  What should I do to make them like me?"
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Read this thread in Mechanics it describes the diplomatic rules in detail:  http://aurora2.pentarch.org/index.php/topic,1613.0.html
In general, you should make the best diplomatic team you can and assign it to them on the Diplomacy (ctrl-F5) screen.  In addition, you should start to initiate communications with them - inability to communicate will be a steady drag on the relationship.  When the "Allow Trade Access" yes button unlocks, flip it to yes.  In addition, keep out of systems in which they have populations - any ships of yours that they pick up in "their" systems will be a drag on the relationship (and vice-versa).

Of course if you don't want them to like you, you can simply start blowing their ships out of the sky  <img src="{SMILIES_PATH}/icon_twisted.gif" alt=":twisted:" title="Twisted Evil" />