At this point nothing is really very certain, but many sources (Anglican and external) cite John Sentamu (Archbishop of (/"for") York) as the most likely candidate, who is Ugandan by origin (so no, not restricted to "English English", although he is a British Commonwealth citizen).
Re approach - Dr. Williams has been working tirelessly as a conciliatory figure within the Anglican communion, trying to hold various sections together. He is also probably best described as a "moderate", seeking a middle line that is broadly acceptable to most. I don't agree with all of his views, but he has been a reasonable spokesperson.
Dr. Sentamu is not this! He is pretty conservative and non-compromising, with very divisive views (he was one of only 4 bishops who refused to sign the Cambridge Accord, which related to the basic human rights of homosexuals). I actually suspect this will count against him in terms of candidacy, since the wider Anglican Church presumably does not hope to fragment itself internally or publicly. Equally, if elected, I strongly suspect his strong views will be a problem for a large number of the congregation (how to say... the general congregation is notably more moderate than many of the Anglican officials, especially on divisive issues like those Sentamu tends to speek on... perhaps it could be said he speaks for the Church as an office, but not for the congregation).
Alternative candidates I've seen mentioned include Rt Rev Richard Chartres and Rt Rev Nick Baines. My personal suspicion is that Richard Chartres has the most chance of not polarizing things to damaging levels, which may count strongly in his favour. It depends on what the committee (this includes the official process, asked in the question) see as important.
Re eligibility, the above link states:
Are all bishops from within the Anglican Communion eligible for consideration as the next Archbishop of Canterbury?
Since the Archbishop of Canterbury is automatically a member of the House of Lords he must, under the law of the land be a British, Irish or Commonwealth citizen. The person chosen will be someone whom the CNC considers to be best able to fulfil the full range of responsibilities of the role, which, in addition to those concerning the Anglican Communion include being Primate of All England, Metropolitan for the Southern province and Diocesan Bishop of Canterbury. There is, however, no rule which limits the CNC to choosing someone who is currently holding an office in the Church of England. Indeed Archbishop Rowan was serving in another province of the Communion when nominated as Archbishop of Canterbury.
Could the next Archbishop of Canterbury be female if the women bishops legislation passes in July?
The next Archbishop will be male, whatever happens in Synod this July. Even if the legislation secures final approval then there are several further steps that will have to occur before it can come into force. It will be late 2013 or early 2014 before it is possible for women to be appointed as bishops in the Church of England.
So basically: must be male, a Brtish/Irish/Commonwealth citizen, but does not appear to need any specific denomination within the Anglican Communion. It seems that the phrasing of the question is an implicit "and must be a Bishop", but I am not 100% sure (having read the briefing documents, available under "Resources" here) that it wouldn't be possible to promote someone into the diocesan role and thus become Bishop and Archbishop at the same time. That said, even if technically possible, it would seem logistically unlikely.