Difficult cold start

I can't help you with not believing me, but the story seems to be changing. We can't see or hear anything you claim. All we have are your words. What was a "difficult" start at 10 Celsius is now "massive" at 30 Celsius. What was running and idling "great" warm is now suspected of having ignition and carb problems, but again, those areas can be improved by a mechanic.
Sorry, I am not saying I don't believe in you. Just thinking that if cold intake would cause this kind of problems, why other cars doesn't suffer from it?

English is not my mother language so I don't always know how to write what I really want to say.

When I started this thread there was spring and temperatures were lower than now in summer. It seems that outside temp does not change this problem, maybe even higher temps make it worse for some reason.

Saying "massive" I mean that has happened twice that I could not start the car at all. Battery ended before it started.
Strangely after winter when I started car first time it started better than now when it has stood a week. Not good but with reasonable starting.

Why I suspect carb is that it really needs pumping gas constantly to keep it even promisising to start. Sounds not getting enough fuel to me. Can't say if there is something wrong with ignition as it is difficult to check how good spark is. I just think that if I convert to pointless it would solve ignition problems if it is the cause. And changing starter to new one would solve possibly starter problems. Those are not so expensible components that I am ready to invest to them even it would not solve problem, but after that I can be rule those out.

Forgot to say that I also tried with helper battery connected to main battery with cables. Trying to rule out voltage drop if old battery is not in good shape, but it didnot help at all. With digital multimeter it is hard to measure voltage drop when starting and I don't have analog one.

I need to do compression test at first.
Engine runs great when it is warm and it seems to have mostly horsepowers left but of cource it is possible that there is no enough compression in cold if oil has flown away from piston rings.
I don' t know how common this problem is and would it cause bad cold start?