Why bitcoin has 7 transaction per second limit?
It doesn't.
It has a 1 MB per block limit and an average of 1 block every 10 minutes.
Given the typical size of the average transaction, if you divide the block size by the transaction size and divide that result by 600 seconds you'll get an average number of transactions that can realistically confirm per second. That number is less than 7. It is somewhere around 3 transactions per second.
The person that calculated 7 transactions per second made an assumption that all transactions in the block would be a minimum possible size.
Do we have any plan to increase this limit any time soon?
Bitcoin is a decentralized peer-to-peer consensus based system. Making changes to the consensus rules is a difficult thing to accomplish since there is no authority that can force everyone to accept what anyone else says. If a consensus is reached among an overwhelming majority of users to make a change, then a change can happen quickly. If a consensus is not reached among an overwhelming majority of users, then a change may never happen.
Developers and users have been discussing this since late in the year 2010.
I mean, 7 is very small number, you don't expect many people to use bitcoin if every second can only process 7 transactions.
Not all transactions have to occur on the blockchain. There are off-chain solutions available. There is also a possibility that consensus could be reached eventually to increase the number of transactions that can confirm.