Given a travel related situation, and given a specific question about the situation, summarize the question into a title

[EX Q]: A few weeks ago, I booked a flight with Transavia going back from Prague to Paris on the Wednesday 10th June 2015.
Yesterday, I received an email saying "your reservation has been updated, click on the following link to see the new time for your flight" and on the linked web page, the flight appears to be on the 12th June.
I have not acknowledged the change yet.

Changing the "time" of the flight by 48 hours seems a bit extreme to me.

Is that legal at all? Is there any procedure to ask for compensations for the additional time off work I'll need to take or for the extra hotel nights ?

[EX A]: Flight rescheduled, what are my options?

[EX Q]: Last time I visited the UK,
it took 3 hours to get through the immigration queues.

I recall seeing signs saying something like:

"Registered Travellers from [list of countries] can use the EU/UK lines."

I have another trip the the UK in a few months,
and I am really dreading the giant queue, especially after a 17 hour flight.

So I am looking up how to become a Registered Traveller.

It says:

Apply online for Registered Traveller membership. ...
You'll get a decision on your application within 10 working days. ...
If your application is accepted, the next time you travel to the UK you must go through the 'other passports' lane and fill in a landing card.
The immigration officer will check that you meet the criteria and tell you if you can become a member. ...

So does this mean that being accepted at point 2, isn't a real acceptance.
You get the real acceptance the first time you enter after applying, using the 'other passports' lane (i.e. the non-UK/EU line).
And then after that if you visit the UK again (assuming all successful), you get to use the EU/UK lane?

(I mostly just want to know if I am understanding it right. I think other things mean it just isn't financially worth it to me to become a registered traveller. I'ld need to pay for a Visa since I've not visited 4 times before)

[EX A]: Is it possible to use UK/EU lanes as a Registered Traveller the first time you enter the UK after applying?

[EX Q]: My family and I are flying to New Zealand (AKL) from the USA (LAX) in just over a week. We booked 7 seats (in a single booking), but when I check the American Airlines website it says we don't have seats assigned, and recommends I select seats. The 7 of us are Mum and Dad (my wife and I), 4 kids (16, 14, 13, 5 years old), and our friend.

When I go to select seats there is only two areas that have a block of enough open seats for 7 people to at least sit close together, however more than half of these seats cost (approx $86-$120 USD each).

Now we don't care where on the plane we sit, we just want to sit together as a family, but can't afford to pay another ~$500 USD to select specific seats.

Are we likely to be seated together anyway if we check-in together? Or are we just going to get random open seats?

Our flight back is on United and we were able to select seats together on the United website without incurring any extra charge.

Here is a screenshot of some of the available seats, to show what we've got to work with currently.

[EX A]:
How to seat family of seven together on long-haul flight?