Given that Bitcoin has a 1mb block size limit (approx. 2k transactions processed every 10 minutes), would I be correct in saying that as soon as the world will start using BitCoin more frequently to do what currency is intended for, purchasing of goods and services, then the number of transactions will be so large that the backlog will flood the system?

Maybe, maybe not. As transaction volume increases, since there is a limited supply of block space, users must compete for block space by increasing their fee rate in satoshis/kB. This might lead users to try to utilize less space by consolidate multiple transactions for example, or utilizing methods like segregated witness. It might also lead to off-chain transactions for small items that do not need to be broadcast to the blockchain if they are part of a group of many transactions over time.

Is there a possibility to enhance Bitcoin nodes so as to increase Bitcoin's block size?

This would require consensus from the network. Also, there are trade offs for increasing block size, so it is not necessarily an enhancement to do so. With larger blocks, propagation delay within the network and validation time becomes a problem and fork rate increases. It could also lead to miner centralization because they have the network resources and computing power to mine, transmit, and verify blocks more quickly. so unlimited block size increase is not considered a good scaling solution.

There are many potential improvements that can be made to help Bitcoin scale such as increasing full node efficiency: e.g. signature checking, block validation, etc. and off-chain transaction networks such as the lightning network.

See https://en.wikipedia.org/wiki/Bitcoin_scalability_problem