It doesn't explicitly say that it has wireless, but I really cannot imagine a modern laptop selling for ~£400 would not have it. As you say, other similar models have it, so I expect they've forgotten to list it. Perhaps best to ask just in case?
The T4400 isn't a bad processor even if is a little old now. It will run 'everyday' tasks easily, but of course the i3 would be better still (and comes with marginally better graphics). Just depends really on whether your needs really warrant the extra speed and cost- or perhaps you just fancy the latest and greatest?