Hi we did a double storey extension and quite a bit of refiguring of the space - we had a front sitting room, 1 main bedroom and 1 single room that weren't touched - everything else was included in the building works.
Family of 5 (3 primary school children at them time). Ours took about 6 months and we lived here throughout. If we could have rented somewhere locally cheaply, I would have done that - but we were looking at in excess of £10k plus a 2nd lot of bills and it was just too much. I don't think living here slowed the build down at all, I was usually on hand to ask questions / check things / point out issues that could be solved quickly. I think as long as you have good builders, it shouldn't matter.
Kitchen - we had a slow cooker / George Foreman / microwave for meals, had made & frozen lots of meals beforehand (plus takeaways, obviously!). Also had one of those little plug in single rings which was very handy. Just had to be organised and a bit more inventive! Washing up in the bath wasn't as much fun!!
Yes to the dirt and dust, it will get everywhere even if you have dust sheets taped to doors etc. Include a new hoover in your budget, you'll wreck the one you have. We also rented a storage unit - so all our furniture, other than the essentials went into storage to protect it, along with lots of kitchen stuff etc.
It was worth it in the end!