"controlled airspace" - means an airspace of fixed dimensions that is so specified in the Designated Airspace Handbook and within which air traffic control service is provided.
-- CARs 101.01

Classification of Airspace

There are many different sorts of named airspace (see CARs 601.01 if you want a list), but every portion belongs to one of seven classes, A through G, each with different rules.  For a full explanation of the rules for different classes of airspace, read CARs 601.02 through to 601.09. The list below may help you remember some of the requirements, based on the letters of the airspace.

A t and Above 18,000' asl.  Airliners and other IFR traffic
B etween 12,500' and 18,000' asl.
C learance required to enter
D ialogue required -- Don't enter without talking to the controller first.
E asy for VFR aircraft - you don't need to talk to anyone. Everyone gone home from class D.
F ancy stuff - special use airspace
G eneral uncontrolled airspace

Classes A through E are controlled.  Class F can be controlled or uncontrolled.  Class G is always uncontrolled.

Notice that the difference between C and D is that you need a clearance to enter class C airspace, but two-way communication is all you need to enter class D.

Weather Minima and Special VFR

To fly VFR in controlled airspace,  you must maintain 500' vertical separation from cloud and one mile horizontal separation from cloud, and have 3 miles forward visibility.

If the weather is below those VFR minima, CARs 602.117 still permits you to fly in a control zone, by requesting special VFR. To request special VFR, you must have 1 mile in-flight visibility, and the tower must also be reporting 1 mile ground visibility.  All you have to do to receive special VFR is ask for it.

For example, you listen to Kelowna ATIS Charlie, and the visibility is 2 miles in mist.  
You: Kelowna Tower, Foxtrot Juliet Delta Sierra with Charlie
Tower: FJDS, Kelowna Tower
You: Tower, Cessna 172 FJDS  ten miles southwest, four thousand five hundred, request special for landing.
Tower: JDS, altimeter 29.94. Special VFR is approved, runway 15, cleared right downwind, report the bridge.

If you didn't say you had the ATIS or include the words "request special" or "request special vfr" in your transmission,the conversation would go like this:

Pilot: Kelowna Tower, Foxtrot Juliet Delta Sierra
Pilot has omitted the ATIS identifier.
Tower: FJDS, Kelowna Tower, Kelowna weather is below VFR minima, only IFR or Special VFR traffic is permitted.
Because the pilot did not indicate he had heard the ATIS, the tower must repeat that information.
Pilot: Tower, Cessna 172 FJDS ten miles southwest, four thousand five hundred, for landing.
Pilot does not say the magic words.
Tower: JDS, Kelowna weather is below VFR minima, only IFR or Special VFR traffic is permitted. What are your intentions?
Tower is hinting.  
Pilot: Uh, I guess we'll go back to Penticton.
Pilot doesn't get the hint.
Tower: Roger, Kelowna altimeter 29.94.

You really hear conversations like that.  Sometimes they go back and forth for some time before the pilot either remembers the magic words, or gives up and goes away.

Sometimes your request for special VFR will be turned down.  Either the controller does not feel that any more VFR traffic can safely operate in the control zone given the current conditions, or the controller has inbound IFR traffic.  In either case you can ask again later.

If you do request and receive a SVFR clearance, you must remain clear of cloud, and if transiting a control zone (not landing there) you must maintain 500' agl.  At night you may request SVFR, but only for the purpose of landing.

Student pilots may not operate in SVFR.  A student pilot permit says "day VFR only" and that does not include special VFR.

If the weather is really bad, you shouldn't be flying, as this joke illustrates.

Question-by-Question Explanation of Controlled Airspace

13.01 To answer this one, you need to know the definition given in CARs 101.01, reproduced at the top of this page, in italics.
(1) Control zones are only one type of controlled airspace, and there aren't any regulations we refer to specifically as "control zone regulations."
(2) Security regulations of one sort or another are in force everywhere these days, even at K-Mart. They don't have anything to do with controlled airspace.
(3) Special VFR flight is only permitted in a control zone -- there is no other place that SVFR is permitted.  But if the weather is good, you don't have to be under SVFR to operate in a control zone.
(4) Right out of the CARs: "an air traffic control service is provided."

13.02
(1) As stated in CARs 602.114 for controlled airspace
(2) Those are the uncontrolled airspace minima.
(3) Vertical cloud clearance in Canada is always 500'.
(4) Vertical cloud clearance in Canada is always 500'.  Three miles is the visibility requirement in controlled airspace.

13.03 A low level airway is Class E airspace. VFR traffic does not  need to contact the controller, or be on frequency, but ATC service is provided to IFR traffic. As it is controlled airspace, you require controlled airspace weather minima.  Another place you find Class E airspace is in a Class D control zone, after the tower closes for the night.

13.04 Controlled airspace requires controlled airspace weather minima.

13.05 CARs 601.08 requires you to have an ATC clearance before entering any part of the Class C control zone.

13.06 CARs 602.117 requires at least 1 mile visibility for airplanes under Special VFR.

13.07 Helicopters may have half the airplane visibility requirements, so 1/2 mile is correct.

13.08 Special VFR exists only in control zones, so if you are under SVFR, you must be in a control zone.

13.09
(1) There is no control tower in an Aerodrome Traffic Zone.
(2) Yes, you need permission prior to entering.
(3) The circuit is inside the control zone. You must call outside the control zone.
(4) Before not after.

13.10 See CARs 601.07.
(1) Three miles visibility is required in controlled airspace, not five.
(2) Even gliders and balloons occasionally make flights inside class B.
(3) There is no such thing as a Class B Airspace Endorsement.  Canadians don't have endorsements. An endorsement is an American concept.
(4) You require an ATC clearance to operate in Class B airspace, and the flight is considered to be CVFR (controlled VFR).

13.11 You require a clearance in order to enter the control zone. Despite the proverb, it is much easier to get permission to enter a control zone than forgiveness for entering without clearance.
(1) You can't call for clearance to enter after entering the control zone.
(2)  Ten miles is a bit far. You might not even be on their radar yet. One to three miles outside would be better.
(3) As long as you have permission before crossing the invisible line, you're okay.
(4) A control zone typically has a three to five mile radius.  The circuit is well inside the zone, so if you waited until right before joining, you would already be inside the control zone.

13.12 This is a nasty question.  You can argue for all the choices being at least slightly wrong.  The only way I know for sure that choice (3) is correct, is that the reference for the question is CARs 601.08, which is about obtaining a clearance and maintaining contact, not about weather minima.
(1) It is true that you must exit the airspace if the weather deteriorates below VFR.  This is the wrong answer because you can't be otherwise authorized.  If you're VFR you need 500'/1 mile/3 miles in controlled airspace, and it's not a control zone, so you can't get SVFR.
(2) A clearance is always required in Class C airspace, not just in class C control zones.
(3) You must maintain a "continuous listening watch," while in class C airspace, but if you only have one radio you may ask for and receive permission to leave the frequency briefly, in order to amend a flight plan, call your company, monitor ATIS, or the like. You could even arrange in advance to enter the airspace without a radio, for example if you were coming to get your radio fixed at the maintenance facilities at the class C airport. One could argue that because this answer choice says "establish and maintain" communications, and the question says "operating within" the airspace, that this answer choice is not quite correct.  You should of course establish contact before you are within the airspace.
(4) "Radar Service" is not an agency, but a service provided by ATC.