It is believed that Bitcoin halving is an event that happens every four years in the crypto industry
Not in "crypto industry", halving is a Bitcoin related event and some altcoins that copied Bitcoin also follow the same thing but may have different intervals.
It is also not "believed" to happen every 4 years, it is part of the consensus rules and must happen every 210000 blocks that happen to take about 4 years.
Since Miners rewards is being cut half during the halving, do they still continue in the number they were before the halving?
This is the 4th halving we've had and so far the hashrate has only grown, meaning the number of miners has grown. The reward has gone down from: 50 > 25 > 12.5 > 6.25 > 3.125
Some miners may shut down and go away if the operation is not profitable enough for them. But the total hashrate is important to us not these small changes.
Does all miners receive equal rewards? or the reward differs base on who solves the algorithms first and a transaction is confirmed.
When a block is found, there is a reward that can not be bigger than the predefined amount. The miner that found that block will receive all of it. However, since nowadays mining is like a cooperation through "pools" there are multiple miners that find a block so they split that reward amongst themselves based on their amount of contribution.
I thought the price will not affect miners since they are getting fixed rewards from the halving, or is it that if the price of Bitcoin reduces the transactions fees reduces as well?
The reward is in Bitcoin while their cost of mining (electric bill, employees' salaries, taxes, etc.) is in fiat so how much 1 bitcoin is worth affects them.
I assume that it is impossible for all miners to stop mining at the same time without a cause except if there by any complications in the mempool which is rare.
Mempool is not a singular place to have a "complication" and have a global effect; each node has its own mempool and not to mention to find a block you don't necessarily need mempool, the block can be empty.
Does it means that all miners must belong to a mining pool?
They don't have to, they can "solo mine" but they'll have to run their own full node and monitor a lot of things. So it is easier to join a pool specially if their hashrate is too low to find a block often enough.