If a solution is found by a miner, does the miner have the control to which nodes is it broadcasted?
Certainly, they can control the first level of peers they broadcast a solution to. However, they have no control over which peers will receive the block from the peers they have sent it to.
It is in a miner's best interests to broadcast it to as many nodes in the network as possible.
If it is broadcasted based on the location of miners, then won't all the miners in the pool have an intrinsic advantage of their pool peers validating the solution?
There are two kinds of miners in a pool - large scale mining operations with mining farms occupying the same physical space, and smaller scale miners who have anywhere from 1 to a few thousand miners who connect to the pools from anywhere around the world.
These mining devices receive work instructions, usually via a protocol such as stratum - once any device in the entire pool discovers a solution, the pool immediately instructs all devices connect to it to mine on top of this new block. Miners that are a part of that pool will then begin mining the next block, likely even before most other pools have finished receiving and validating the newly found block.
Since sharing your block with as many other nodes as possible is key to its acceptance in the event of a competing block, there are special solutions solely dedicated to broadcasting blocks, such as https://bitcoinfibre.org/.
Let's take a case when there are two solutions being broadcasted at the same time, one from the USA and another from China. Since, a lot of miners are there in China, Mongolia, Russia etc. doesn't miners in China have a better chance of getting consensus?
Pools will generally mine on top of the first block they see. However, consensus will only be achieved when a new block is found on top of one of the two competing blocks.
Also, what do we mean by consensus in the above case? Let's say the USA solution reached 20% of the active miners and the Chinese solution reached 80% of the miners. As per my understanding even the USA solution could reach more than 51% consensus(more than 10% of globally active miners agreeing with the solution). Shouldn't there be a threshold on the minimum number of global miners agreeing with your solution given this large pools existence?
Consensus here is not dependent on how many nodes you are able to broadcast your solution to, but depends on the next block to be mined. If block N has N_USA and N_CHINA, and block N+1 refers to N_USA as the previous block, block N_CHINA will be discarded as block N_USA is part of the longest chain, regardless of how many nodes had received N_CHINA before N_USA. Until block N+1 is found, both blocks are valid.
This is known as selecting the longest chain, or more formally, the chain with the most work.