Having arrived at Malta airport February 1, 2016, there was a booth (I think towards the right hand side from Arrivals) where I was able to purchase a Tallinja card for €21 for 7-days. The booth also accepts Amex cards.
This covers the whole of Malta and Gozo (Għawdex). Whether or not this can be topped-up I'm not sure.
Pretty much every card follows the standard ISO/IEC 15693 or ISO/IEC 14443 which means they operate on 13.56 MHz and will potentially interfere with each other. You might be lucky here or there but in general any two contactless cards will cause interference.
You can register for a Tallinja Card online, using the official website. The card will then be shipped to your address. Otherwise you can collect an application form from the ticket booth, fill it in and hand it back to the booth. There is one such booth at the airport.
Quoting from the Tallinja FAQ:
How can I obtain a tallinja card?
One can easily ...
Yes, it is possible and it is very easy. This webpage on publictransport.com.mt (retrieved in June 2018) includes two sales points in Malta International Airport:
Agenda Bookshop (Departures Hall),
WHS Express (Arrivals Hall).
This latter in particular is only a few steps before the exit on the bus terminal, coming from Arrivals. Twice in the latest year I ...