As the number of Public keys available in BlockChain increases, does it cause extra risks for private key's security? Any bitcoin address eventually use its public key when spending its BTC. And as we all know, bitcoin address is produced from a public key by utilizing one way function. What is advantage of using bitcoin address ? 
Does it make any address anonymous till spending BTCs ?
While the block-chain size increases over the time, there are lots of public keys available, and some fraudulent person maybe try to estimate private key by enabling brute-force method. 
Does it make any disadvantage or cause extra risks the whole system ?
Any bitcoin address eventually use its public key when spending its BTC. And as we all know, bitcoin address is produced from a public key by utilizing one way function. What is advantage of using bitcoin address ?


A bitcoin address is not technically broadcast and included in the blockchain database until it is funded. So spending is irrellevant, because it would become public the moment it is funded. 

Simply put, it's not "live" until it is funded. It's just a place card, if you have the private key, any funds sent to that account can be later spent, and upon funding, it would be public, regardless of whether there have been outbound transaction. 


Does it make any address anonymous till spending BTCs ?


Spending, or Receiving, broadcasts the address with any transaction made through nodes, which confirm the transaction as valid and not duplicate. For each block that is found where the transaction you made is included, given you have included a fee which the nodes accept as "fair", is called a confirmation. 


While the block-chain size increases over the time, there are lots of public keys available, and some fraudulent person maybe try to estimate private key by enabling brute-force method. Does it make any disadvantage or cause extra risks the whole system ?


No. There is no way, currently, for anyone to brute-force an address's private key. There are statistics and charts, but if you used the worlds fastest super computer, you would need millions, millions of years. It simply, is not feasible. Quantum computing could change that, but the reality is, quantum computing is not even yet in its infancy. (Not that we know of). It is way off in the distance, if ever. 

That said. The reason cracking a private key from a public key is "impossible", is this:

Think of your Private Key as the Question. 

Your Public Key, is the Answer. 

It is not the other way around. 

So if your public key is 100 (Shortened for this example) you know the answer. That is public. 

To crack, you need to now figure out the question. 

Is the question What is 10x10?  Or 1x100? Or 101-1? 

Simply, there are far too many possibilities, in terms of questions, to any "answer". Cracking, brute-force, I don't think so.