1. Hotels around the airport tend to be much cheaper than in the city. They also tend to be of a more decent size, cleaner and generally nicer for the same amount of money.
However, you have to be prepared to travel back and forth each day. That, depending on how you were planning to spend your days and evenings, might work - might not. If you plan on staying out till very late (past 11pm) then airport trains stop running by then, for example. If you plan to stay within sensible hours (i.e. 8am to 10pm) then you should be able to pull off an airport hotel - but be prepared to spend more time getting to/from the airport, and remember to factor in the cost as well.
2. A lot of people (especially young people) speak/understand English. (Not just in Tokyo, as someone else said :/) Tip: If you find that the other person doesn't understand what you are saying in English, it is often helpful to write it down. This is because non-English speakers find speaking and listening much more difficult than reading and writing.
3. As for your question, "What airlines would you lot recommend that'd fly from manchester, have laptop power sockets, and have good enough seats for sleeping?"...
There is no easy answer. Most economy class tend to be very similar to each other - i.e. very sparse in features and packed as much as they can get away with.
To fly from Manchester, you're looking at a minimum of one transit, whether you do it in London (for BA/Virgin/ANA/JAL), Paris (for Air France), Amsterdam (for KLM) etc. Of the airlines that are likely to be the cheapest (that would be the European airlines), I'd say Air France is probably your best bet. I've had some less than stellar experiences on KLM and Lufthansa gets a very bad rep for their economy class.
No airline so far has widely available power sockets in Economy Class. You'll have to supply other forms of entertainment once the laptop battery runs out, I'm afraid - so far, power sockets are more or less reserved for Business Class or higher. Maybe you can ask one of the flight attendants whether you can use the power outlets in one of their Business Class seats to charge your laptop after it has run out - might work, but they might also say no.
Seats for sleeping - basically, don't count on it
Your best bet is (depending on airline) either phoning ahead to request/reserve a bulkhead or emergency exit seat, or turning up at the airport super-early to request such a seat. But try not to get a window seat on an exit row, because the door often has a large protusion into the cabin which means legroom is no better than other seats. The very best seat IMHO is an emergency exit aisle seat - that way, you're not sandwiched between people, and you get large legroom.
Also, the downside of personal TVs is that they often have the equipment box underneath the seat so it tends to occupy your legroom underneath the seat (if you don't manage to get a bulkhead or emergency exit seat).
If you tell me your exact dates, I might be able to see which airlines are available for how much.
4. If you haven't decided whether to go to Tokyo or Osaka (or if you can go to both), Nara (40mins by train from Osaka) is very nice. Plenty of historical and traditional stuff, as well as a very nice deer park. Perhaps not worth changing the destination just for Nara, but worth considering if you haven't already decided. Also bear in mind that Kyoto (also very traditional and historical) is close to Osaka as well.
I'd say - if you want historical buildings, temples and atmosphere, I'd be inclined to say Osaka. If you want to mainly experience the full-on pace of city life in Japan, Tokyo will probably be better.