car struggles to start when cold

i dont use a key because my steering collum is chipped so i have to pull on the little rod, but sometimes it doesn't like to start up. Could this be the starter, i'm pretty sure it's the same one that came stock

If it turns over, it's likely not the starter, unless it's turning over slow (and that's also not always the starter). Does it run okay once it's started?

If it does turn over good, then you can pretty much rule out a starter issue. Check the fuel filter (actually replace it, they're cheap) as a plugged filter will most definitely cause hard cold starting issues (among other things). Also, replace your air filter and check the ignition system (cap, rotor, plug wires, spark plugs) to ensure everything here is good to go. If not, then this could cause your hard start plus your low vacuum condition (assuming there's a misfire) leading to your A/C issue posted on another thread.

I replaced my fuel filter, spark plugs and wires, Bought a new K&N air intake filter, I'll prolly open the cap to see if the squares are clean. but now when the engine is war is runs perfect, but when the motor is cold it starts fine but when i put it in reverse or drive it bogs down and stalls if i dont floor it, but some times it stalls out, but it only does this when cold.... and my ac still doesn't blow cold when i give it gas and when it's on and my car is in idle it runs horribly