What is an ATC clearance? Does a VFR flight have to get a ATC clearance? 1)
Do all flights have to get an ATC clearance to fly in controlled airspace such as class C airspace? I know that IFR and VFR flights are provided with ATC service in class C airspace, but I am not sure that receiving ATC service means an ATC clearance must be obtained. And if so, should VFR aircraft also get an ATC clearance like an IFR clearance that is given to a pilot before take-off including clearane limit, route, level, squwak, etc?

2)
What is an ATC clearance? 'ICAO Annex 11' defines an ATC clearance as an "Authorization for an aircraft to proceed under conditions specified by an air traffic control unit." And, also states that an "ATC clearance shall indicate a) aircraft identification as shown in the flight plan, b) clearance limit, c) route of flight, d) level(s) of flight for the entire route or part thereof and changes of levels if required and e) any necessary instructions or information on other matters such as approach or departure manoeuvres, communications and the time of expiry of the clearance."

I think it refers to the IFR clearance given to pilot before take-off.

Does it mean that an ATC clearance always includes all these items such as route or level? If the ATCO instructs a VFR pilot to maintain 5,000ft for separation with IFR, is it just instruction because it doesn't include a clearance limit and route?

In the same vein, is a take-off clearance a type of ATC clearance? It doesn't include some items such as route. But the definition of an ATC clearance states that "The abbreviated term “clearance” may be prefixed by the words “taxi,” “take-off,” “departure,” “en route,” “approach” or “landing” to indicate the particular portion of flight to which the air traffic control clearance relates."
All IFR flights require a clearance in controlled (class A-E) airspace. Clearances aren't available in uncontrolled (class F-G) airspace.

VFR flights in certain airspace (ICAO: class B-D, FAA: class B only) require a clearance and may be referred to as CVFR. This clearance will be much simpler than an IFR one, though.

The purpose of an IFR clearance having a limit, route and altitude is so ATC knows what the plane will do if communication is lost and therefore can maintain proper separation of other aircraft. This detail isn't required for a CVFR clearance because a VFR pilot is required to be able to provide his own separation anyway, so the VFR lost comms procedures are much simpler.

ATC can amend a clearance, in which case they only say the items to be changed, or they can cancel the old clearance and issue a new one from scratch. Which they choose depends on how much is changing and why.

An instruction may authorize a (usually brief) deviation from a clearance, e.g. to avoid traffic or weather. ATC can give instructions to VFR flights without a clearance to amend, though, and this doesn't create a new clearance, so they're something different.