new rebuilt engine? blue smoke?
most likely it needs to be broke in, after it runs a bit and gets hot the oil rings should seat and the smoke should go away.
As for the pressure in the radiator? that is normal once the engine gets hot, there will be pressure build up when it heats up. What i would do is remove the cap, crank the engine and let it run till it gets up to temp, monitor it, watch the water/coolant during this process and see if there are alot of air bubbles in the coolant/water while it is running. If there are alot of bubbles then there is a compression leak getting into the cooling system, possibly caused by a bad head gasket or cracked head/block.
Note: if it is a rebuild? those thing should have been checked before reassembly of the engine. You might also want to recheck the torque on the head bolts, mazda 2.2's head bolt torque should be:
"Cold 81 to 88 Nm (60 to 65 ft lbs)"
"Hot 95 to 100 Nm (70 to 74 ft lbs)"
The compression for a new engine should be:
"1131 kPa (164 psi) @ 270 rpm"
your readings are below that which makes me wonder if there is something wrong with this engine internally.
I would record all this info and inform whomever you got this engine from that it is not meeting the requirements designated in the manual.
They should instruct you on what to do at that point, you don't want to void any warranty you might have with this rebuilt engine so do what the rebuilders suggest 'by the book'. Then if it winds up being a bad engine then you should get a good one. Be diligent with them and don't let them steer you away from the facts you find, if they gave you a bad one then make them make it right.