Hello all.

I'm requesting your few second answer if you know how to solve this issue that kill me softly,
Sparks, coil sparks and head gasket changed.. the engine has misfire on start, rpm fluctuates, car shakes and then after 30 seconds or so idle drop back down idle is smooth afterwards and misfire is gone.

Please help..

 

Mine will do that if I mess with the programming too much, meaning make a mistake it'll go super rich and run very rough. I assume you have not tinkered with it so I suppose I would get a tool to read what it happening on start.
A simple obd dongle and the Torque Pro app will do it. This is the one I used to use and it works fine: Not the best tool, but good enough, and for the price you can't beat it.
Then you program it to read Injector Pulse Width, Commanded Lambda, Fuel pressure, Spark timing, RPM, MAP, Throttle position, Eng temp, which I think should do it? Turn the ignition On, get the app to read the data, then fire it up so it sees everything from before start, during crank all the way to running fine.
Then you can see if anything doesn't look right. It's been a while since I used that app but I believe it saves the data to a .cvs file, which I then plugged that into Excel and make a chart so you can see it. Post a screenshot of said chart(s).

When cold the engine will be in catalyst heating mode, which on my car lasts ~20-30 seconds. It's also when the O2 sensors are not working so the car is in "open loop" mode. It's running blindly without O2 sensor feedback. Not a big deal, but things can happen. Say for example you have an intake air leak. It doesn't know that so it supplies the normal qty of fuel and it runs lean. Then the O2 kicks on and sees it's lean and gives you extra fuel and it starts running normally. O2 sensors typically take 30-90 seconds to start working but it varies eng to eng.
Plus you need to post when this started to happen. Like first thing after the head gasket, or xx time after, or before? Did it come on suddenly, or slowly get worse? Does it only do it when cold? Or maybe the colder it is the worse it is? And you need to post if you have any diagnostic codes. The aforementioned OBD tool can do that. Most codes do not trip a check eng light (CEL) so there may be codes but you have to look.

In cat heating mode there are two things taking place; one is a slightly leaner fuel mix which should be a non-issue unless you have an air leak making it worse. The other is extremely retarded spark timing. The spark timing is what makes it rather loud for ~30 seconds after a cold start. The retard heats both the eng and exhaust much faster than normal spark timing. This is a smog function and not good for the engine, imo, but it is what it is. If this spark retard isn't working it will not make the eng run rough, if anything it runs better, but I mention it just as an fyi. The fuel mix on the other hand will make it run rough. It can, on my car, dump in twice as much fuel and idle pretty rough, but I won't get a check eng light. At some point, like 3x as much fuel, it'll throw a code but it takes a lot to give me a CEL, mainly, imo, because it doesn't know it's doing anything wrong. At some point, >2x the fuel needed, it'll be bad enough that it misfires and it should see that.
So get that OBD dongle thing, or something that can read codes and see live data, and post results. I use HP Tuners to see all this data, which is day/night better at it but it's also ~$400US for the dongle. Then if you want to make changes to the cars programming you have to pay another $300. Ouch, but it was worth it for me.

 

Start with getting a simple Bosch 1150 scanner like this. They’re about $55 right now and can see codes, data, and graphs. Simple and effective!

Get a graph of the ignition advance of startup.