A) How often does a Meterological Report (METAR) come out?

On the hour or as required with the issue of special.  

B) How often does a Terminal Aerodrome Forecast (TAF) come out?

Short answer,  the standard is every 6 hours (at 0600, 1200, 1800 & 0000 Zulu).

Longer answer, if the airport is not operated 24 hours the times can differ. For example here at Whitecourt Airport they are issued twice a day at 1400 & 1900 Zulu.

C) A TAF is considered accurate for how many miles away from the airport?

A TAF is considered to be accurate for a radius of 5nm from the center of the runway.

D) In a METAR what is considered a cieling? 

Cloud covers of Broken (BKN) or Overcast (OVC) are considered cielings. Don't forget a Vertical Visibility (VV) is also considered a cieling.

E) In a TAF what is the difference between FM and BECMG? 

Both signify an expected permanent change in the forecasted weather. From (FM) will give a time that change is expected to happen. For example,

FM032200 They are forecasting a permanent change beginning at 2200 zulu on the 3rd day of the month. 

Becoming (BECMG) will also give a time but they are expecting that change to be gradual. For example,

BECMG 0315/0412 means they are forecasting a permanent change to happen between 1500 zulu on the 3rd day of the month and 1200 zulu on the 4th day of the month.

F) What do the following mean;

VCSH     GR     -GS     PL     +FC 

VCSH Showers in the Vicinity
+GR Heavy Hail
-GS Light Snow Pellets
PL Moderate Ice Pellets
+FC Tornado or Waterspout (it's not often you see this one!)