A New Zealand (Football Kingz) were given special approval to put a team in the Australian League back in 1999, when both countries were part of Oceania. It was similar to situations in the MLS (Toronto FC), and the UK (Swansea, Wrexham, Cardiff all play in England, and there's a team near the Scottish border that plays on the wrong side of that line). At the time Australia were helping out a member of their own confederation. When the A-League was revamped from clubs to franchises in 2005, the Kingz were rebranded as New Zealand Knights were given a license. Australia were still part of Oceania. When the Knights went under at the end of 2006, an 11th-hour Wellington Phoenix bid beat out 1 or 2 Australian bids. Although Australia were then in Asia, I think the FFA were keen to take advantage of marketing opportunites in New Zealand, and were wary of spreading the Australain fan-base too thinly, especially as they were (and still are) struggling to gain a foothold in a market dominated by Aussie Rules, and Rugby League, and also face competition from Rugby Union. They probably would have looked at the crowd-pulling power of New Zealand teams in Australian League (Warriors) and basketball (Breakers). The teams based in Auckland failed to do this, but the Wellington side have largely succeeded.
While they are not yet turning a profit (no-one is), they are one of the few clubs that hasn't needed an FFA bail-out.
Why do Wellington who is obviously from another Confederation get invited to A-League and issue license by FFA but not any other club in its own Confederation?
Because most (if not all, and certainly those within a reasonable travelling distance) members of the AFC have professional leagues. New Zealand doesn't (and won't - I believe this is a condition of FIFA giving permission)
How does admitting a New Zealand club to an AFC association league benefit its fellow members?
It probably doesn't. But then again, would replacing the Phoenix with a team from Canberra benefit other Asian countries? By and large, the FFA and the club itself consider the Nix to be an Australian franchise based in Wellington, although they've yet to convince the AFC of this.
Doesn't this also unfair practice by New zealand with respect to its fellow Oceana Confederation lack of similar opportunity? A-League as a one player limitation rule while Oceana players are considered foreign players with greater numbers permisible.
Australia leaving the OFC benefitted New Zealand in terms of qualifying for FIFA tournaments. That said, it hasn't been one way traffic and other Oceanian countries have also benefitted - Tahiti went to a youth World Cup last year (U-17?), and a Papua New Guinean club won the OFC Champions' League and played in this year's World Club Cup.
New Zealand football benefits by gaining exposure in the competiton for fans and players with other sports.
New Zealanders, like other Oceanian players, are considered foreigners in the A-League, although the Phoenix have dispensation to consider both NZers and Australians as local players (a sticking point with the AFC). Of the current squad, there would only be 4-5 New Zealanders who are regular starters, and at least 2 of them have played for A-League clubs across the ditch previously (and a 3rd played for the Knights). For comparision, there are at least 4 Kiwi internationals currently at Australian clubs.
However, there is a noticeable dearth of Oceanian imports in the league.
On the other hand, the Phoenix have signed Asian players, in fact probably more so than many Australian clubs. The Roar and Newcastle both had a Korean each, Sydney still do, and then there's Surat (and Sutee's 'guest' stint) at the Victory. I can't name any others offhand. The Phoenix and the Knights used Lei Lei Gao for a couple of seasons, and Jiang "Jonny" Chen was with the club last season (both Chinese). They also trialled Indonesian Bambang Pamungkas for the current season, but reportedly couldn't match the money of the Indonesian League (The A-League is salary capped)
If AFC would like to embrace Australia into its arms, why don't Australia reciporcate?
Australia made an application that was obviously mutually beneficial at the time. I think there is still a fair bit of resentment within the AFC of Australia's membership, particularly in West Asia, who see them as poaching one of 'their' spots at the World Cup. New Zealand probably didn't help the situation (or that of the Phoenix) by knocking out Bahrain last time either.