What exactly is the 'shuttle effect' in sulfur batteries?
OP's title indicated OP is looking for the real mechanism of  the Shuttle Effect in $\ce{Li-S}$ batteries. Yet, OP is asking different questions in the text body. I'd try to address as much as possible in this answer.

A most recent review article (Ref.1) states that:


  Lithium-sulfur ($\ce{Li-S}$) batteries are one of the most promising batteries in the future due to its high theoretical specific capacity ($\pu{1675 mAh g−1}$) and energy density ($\pu{2600 Wh kg−1}$). However, the severe capacity fading caused by shuttle effect of polysulfide needs to be addressed before the practical application of $\ce{Li-S}$ batteries.


To understand what is the Shuttle Effect, OP need to first understand the working chemical mechanism of $\ce{Li-S}$ batteries, and can take a head stat in that direction with this article about Lithium–Sulfur Battery, which gives a fair description of the chemistry involve in the battery. The same Wikipedia article simply described the Shuttle Effect as follows:


  The lithium polysulfide $\ce{Li2S}_x$ ($6 &lt; x &lt; 8$) is highly soluble in the common electrolytes used for $\ce{Li-S}$  batteries. They are formed and leaked from the cathode and they diffuse to the anode, where they are reduced to short-chain polysulfide and diffuse back to the cathode where long-chain polysulfide are formed again. This process results in the continuous leakage of active material from the cathode, lithium corrosion, low coulombic efficiency, and low battery life.


The formation of polysulfide shuttle effect is classified into five steps in Ref.1:


  
  Formation of long-chain polysulfide,
  Detaching of polysulfide from sulfur host,
  Dissolution of polysulfide into electrolyte,
  Migration of polysulfide toward lithium anode side, and
  Reaction between polysulfide and lithium anode.
  


If interested, OP may read Ref.1 and Ref.2, which thoroughly discussed the mechanism and possibilities of how to prevent the Shuttle Effect in depth. For example, one such techniques is modifying the separator, which has been done successfully recently (Ref.3):



References:


Wenchen Ren, Wei Ma, Shufen Zhang, Bingtao Tang, "Recent advances in shuttle effect inhibition for lithium sulfur batteries," Energy Storage Materials 2019, 23, 707-732 (https://doi.org/10.1016/j.ensm.2019.02.022).
Chao Deng, Zhuowen Wang, Shengping Wang, Jingxian Yu, "Inhibition of polysulfide diffusion in lithium–sulfur batteries: mechanism and improvement strategies," J. Mater. Chem. A 2019, 7(20), 12381-12413 (https://doi.org/10.1039/C9TA00535H).
Yanpeng Fan, Zhihui Niu, Fei Zhang, Rui Zhang, Yu Zhao, Guang Lu, "Suppressing the Shuttle Effect in Lithium–Sulfur Batteries by a UiO-66-Modified Polypropylene Separator," ACS Omega 2019, 4(6), 10328-10335 (https://doi.org/10.1021/acsomega.9b00884).