Is it good to lease things from companies?
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It depends of your economy. In the beginning of the game, I usually rushbuy social project that have 1 or 2 BC of social production left.
BTW, rusbuying a social project and a military poject have different timing: rushbuying a social project allows you to change in the same turn the production. Rushbuying a ship is effective only at the begiing of the next turn.
Is that how the AI has built constructors and colony sips so fast and the reason that my treasury is the fullest with 10000?
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Probably. ANd it is 1 000 BC at the beginning of the game, not 10 000 BC. And since you have so much treasuyr, you can use 100% spend rate and be in deficit as long as your treasury is neagtive. It is very help in order to be able to produce a colony ship every 3 turns on Earth.
and why does the ai have a higher score than me in tech but I no less techs than him?
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Are you speaking about total techs or researched techs?