I'm a novice/hobbyist mechanic but recently have been trying to do up my fiesta 2007 mk6.5 (mk6 facelift) 1.6l tdci with about 130k miles on the clock.  

For a bit of context, I have this issue where when I try to turn the car on from cold (usually in the mornings), it takes about anywhere from 1min to 3mins of cranking to get the engine started. After the car starts up, the car runs at about 600rpm for 10 seconds until (what I assume to be) the last cylinder catches and the car then runs at the usual 800rpm. The idle at this point is rough and when I rev the car in neutral it can sometimes sputter (between 850-1250rpm). There is also a lot of white smoke coming out of the exhaust at this point which I think is unburnt diesel (because that's what it smells like). After driving the car for about 5-10mins, all of these symptoms go away and the car drives and idles like a dream. However, the car does sometimes struggle to accelerate up really steep hills now which it never used to.

I've checked the glowplugs and relay, and they are fine. I also recently had a mate of mine have a look at the fuel system and injectors. He said the fuel filter and pump were completely fine and there were no fuel leaks or clogging. He said that one of the injector's o-rings had perished so changed it for me. He also checked the flowrate through the injectors and said that injector 3 seemed to be in the process of failing. He said that injector 3 was letting air back through it when the car is sat for prolonged periods of time. So we are assuming that the reason for the long crank times in the morning is because there is air in the fuel line, which is then being pumped through the failing injector while cranking. Not sure whether these symptoms are typical of a failing injector or whether I need to replace all the seals on my injectors instead. I'm happy with the second option though because that would be cheaper.

I have a few questions before I go ahead and do any work on the car:

1. Are there any other faults with the car that could be causing these symptoms?
2. Is air in the fuel line a failing seal or injector problem?
3. If this is an injector issue, then should I just replace injector 3 or all four injectors? I'm assuming it's probably best practice to replace all four.
4. There are a lot of different types of injectors to buy online (i.e., refurbished, used from a breakers, etc), although I haven't seen any new brand new ones available. Obviously buying used ones from breakers has its issues as well. The engine in this motor is in a lot of cars. It's an EV5/6 engine I believe, but correct me if I'm wrong. So what type of injector and from which brand/what state of 'newness' (i.e., refurbished, used, etc) would you suggest to replacing my current injectors with? Any links to examples would be greatly appreciated.

I'm particularly interested in the answers you all might have for question 4.

There are a number of videos online showing how to replace the injectors for this car. So, ideally what I'd like to do is change the injectors myself to avoid the high labour costs at a garage. But yeah, I just thought it best to ask what you all think before I go ahead and do anything to the car myself.

Thanks in advance for the responses.

For anyone that's interested, I discovered what the above problem was. It would seem that my thermostat was faulty, thermostat was stuck closed. Basically, about 3 weeks ago, my car started overheating like 5 minutes after starting my engine so I went and got the thermostat changed and that fixed the hardstart problem. Now I'm not really sure how the thermostat being stuck shut would cause a hardstart condition but it fixed my problem. Any explanations as to why the thermostat caused this would be greatly appreciated!