You will still see some impact of Iris in Placencia, mainly from Seine Bight village south -- debris, a boat or two capsized, "holes" where houses or buildings used to be, missing palms and other trees. But generally things are getting back to normal, and in the Maya Beach area (north on the peninsula) it looks about as it always did.
Turtle Inn will not open until December.
You can just wait until you get to Belize to buy your tickets to Placencia.
You cannot get from Placencia to Caye Caulker except by going back to Belize City. Occasionally somebody arranges a boat from Placencia to Tobacco Caye, but the usual way of getting there is to go to Dangriga and take a boat from there (US$15) -- I recommend Captain Buck.
There are plenty of nice places to stay in Placencia for under US$80. Tradewinds at south point has the best location in Placencia village and little beach cabins are under US$50 double. Barnacle Bill's has two beautiful cabins on the beach at Maya Beach, in your price range, but it is a little away from things if you do not have a car. Not on the water but nice and newish is Manatee Inn at the north end of Placencia village, around US$35 double.
Belize books and publications by Lan Sluder:
Belize First Magazine (http://www.belizefirst.com
Fodor's Belize & Guatemala Guide (new 4th edition coming this fall)
Adapter Kit: Belize (the first and only comprehensive guide to living, retiring, working and investing in Belize -- a best-seller on Amazon.com)
San Pedro Cool (the first and only visitor guide to Ambergris Caye)
Belize First Guide to Mainland Belize
UpClose Central America
Belize Book of Lists