If the cabins do need both 2.4 and 5Ghz then you do need two AP's (assuming they are off in different directions from each other and one AP would not cover both areas).
With either the AP-114 or AP-135 there are 3 RPSMA connectors that serve both radios so only one ANT-17 is needed and it will txmit both 2.4 adn 5Ghz.
So long as you are getting standard 802.3af PoE on the AP-105 that is fine. There will be no difference between PoE or a power adaptor.
Also, stating the obvious, make sure you have good clear line of sight between the ANT-17 and the cabins. I could not tell what your mounting height is from the photos but the -17 has a slight downtilt so you may want to have it up a little high -- above peoples heads and out of the way say 10 - 12 ft. Also, you might take a look to see what ARM is doing and make sure that it has not turned down the Tx power. You can override ARM by changing the Min / Max transmit power under the RF settings. You can also see what ARM is doing by going uner the Support tab then execute the "show AP ARM ..... " commands.