1. When bitcoin-qt started, full sync will be performed. Say I started my bitcoin-qt, then once the full sync is done, my blockchain is up-to-date, which means, my latest block height is highest number. Correct?
Bitcoin Core will determine if it's the latest block by comparing the block header with your peers.
2. Each node has their own copy of the blockchain. Whenever sync is done, the blockchain in each node will be updated acoordingly. So when the sync is actually performing? Only at the startup? Whenever new block is submitted from a miner? Periodically?
Initial Block Download (IDB) is the process to download the blockchain from the genesis block initially. After it gets to the chain tip, it will verify and process blocks when it gets relayed from any of its peers that it is currently connected to.
3.I am not sure I fully understand here...so how the block height will be synced across nodes correctly? I mean...say..in A node, there r 5 blocks...and new block submitted to this node, and added in that chain, say the block height of this new block is 6...say in B node, there are 5 blocks as well...say new block submitted to this node, and added...then this block height is also 6... So..basically same block height number, but different blocks... wouldn't that be necessary to resolve this somehow?
Nodes will always follow the chain with the highest cumulative POW(POW). If two blocks happens to be found at the same time, a fork is formed. In a perfect scenario, half of the network's nodes will see Block A and half of the network's node will see Block B. Miners will build their blocks on top of the block that they see first. Whichever miner that finds the block on either chain will lengthen the chain and thus increase it's cumulative POW. After which, the new block, Block C which is built ontop of Block A will be relayed through the network. Those nodes which sees Block A will include Block C in their Blockchain and those nodes which sees Block B will discard Block B and include both Block A and Block C in their blockchain.
As such, Block B is out of the equation and the network continues to build on Block C.