Itskells

I finally got a civic 4g it's solid and engine will be swapped in time but I need it running again......
it was running fine till I put a tornado air filter on it and after I butchered my airbix OEM .
I put OEM back to normal and it just got worse
I can start no prob and idle fine sometimes it surges up down up down , but stops when I unplug iacv sensor, still surges a faint bit. But as soon as I get to end of my driveway an pull into Rd it wants to die as soon as I touch gas. Have to feather it like crazy to keep rpms up.and it dies and then battery dies eventually. I do have a bit of white smoke at high rpms if I really stomp on it well when it made it was driving.
I've checked all the usual stuff dizzy plugs. Vacuum. Any ideas and can a head gasket leak without coolant in oil or vise versa . Also my alternator won't keep car running if I disconnect battery cable. Help please