95 mx-5,cel says o2 no output,and ac question?

hey i have a 1995 mazda miata mx-5 1.8L
5 speed when im driveing it for awhile i shut it off and wait like half hour i go to start it and it takes awhile, but if i drive it and turn it off and back on it starts fast.
and when i drive the cel comes off and on through out the day, and the last prob is it runs but hesitates most the time, sometimes its so bad when you try to give it gas it boggs down then i just floor it till it gets to over 4500 rpms then its back to normal, i dunno what my problem is i changed the fuel filter, and the only code came up was o2 sensor no output and im stuck will o2 sensor cause all this


second question ac is fully charged but the ac compressor clutch wont kick on i tryed turning it and it turns? must be the relay
?


thanks soooooooooo much for replys
i love this car its sooooo fast....
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heres what my car looks like what do you think?


http://i128.photobucket.com/albums/p175/celicaboy_87/l_6c2af9d5b1f724ef3bfde24c11c90639.jpg