I'm adding to @Dilip's basic answer, to cover the additional points in your question. I'll assume you are referring to publicly traded stock options, such as those found on the CBOE, and not an option contract entered into privately between two specific counterparties (e.g. as in an employer stock option plan).
Since you are not obligated to exercise a call option you purchased on the market, you don't need to maintain funds on account for possible exercising. You could instead let the option expire, or resell the option, neither of which requires funds available for purchase of the underlying shares.
However, should you actually choose to exercise the call option (and usually this is done close to expiration, if at all), you will be required to fund your account much like if you bought the underlying shares in the first place. Call your broker to determine the exact rules and timing for when they need the money for a call-option exercise.
And to expand on the idea of "cancelling" an option you purchased: No, you cannot "cancel" an option contract, per se. But, you are permitted to sell the call option to somebody else willing to buy, via the market. When you sell your call option, you'll either make or lose money on the sale – depending on the price of the underlying shares at the time (are they in- or out- of the money?), volatility in the market, and remaining time value. Once you sell, you're back to "no position". That's not the same as "cancelled", but you are out of the trade, whether at profit or loss.
Furthermore, the option writer (i.e. the seller who "sold to open" a position, in writing the call in the first place) is also not permitted to cancel the option he wrote. However, the option writer is permitted to close out the original short position by simply buying back a matching call option on the market. Again, this would occur at either profit or loss based on market prices at the time. This second kind of buy order – i.e. made by someone who initially wrote a call option – is called a "buy to close", meaning the purchase of an offsetting position. (The other kind of buy is the "buy to open".)
Then, consider: Since an option buyer is free to re-sell the option purchased, and since an option writer (who "sold to open" the new contract) is also free to buy back an offsetting option, a process known as clearing is required to match remaining buyers exercising the call options held with the remaining option writers having open short positions for the contract. For CBOE options, this clearing is performed by the Options Clearing Corporation. Here's how it works (see here):
What is the OCC?
The Options Clearing Corporation is the sole issuer of all securities
options listed at the CBOE, four other U.S. stock exchanges and the
National Association of Securities Dealers, Inc. (NASD), and is the
entity through which all CBOE option transactions are ultimately
cleared. As the issuer of all options, OCC essentially takes the
opposite side of every option traded. Because OCC basically becomes
the buyer for every seller and the seller for every buyer, it allows
options traders to buy and sell in a secondary market without having
to find the original opposite party.
[...] [emphasis above is mine]
When a call option writer must deliver shares to a call option buyer exercising a call, it's called assignment. (I have been assigned before, and it isn't pleasant to see a position called away that otherwise would have been very profitable if the call weren't written in the first place!)
Also, re: "I know my counter party cannot sell his shares" ... that's not strictly true. You are thinking of a covered call. But, an option writer doesn't necessarily need to own the underlying shares. Look up Naked call (Wikipedia). Naked calls aren't frequently undertaken because a naked call "is one of the riskiest options strategies because it carries unlimited risk". The average individual trader isn't usually permitted by their broker to enter such an order, but there are market participants who can do such a trade.
Finally, you can learn more about options at The Options Industry Council (OIC).