This is a multiple-correct question where we need to evaluate each statement about polymers.

Statement A: The polymerization of chloroprene gives natural rubber.

1. Natural rubber is a naturally occurring polymer. Its monomer is isoprene (2-methyl-1,3-butadiene). The chemical structure of natural rubber is cis-1,4-polyisoprene. $n \, \mathrm{CH_2=C(CH_3)-CH=CH_2} \xrightarrow{\text{Polymerization}} -[\mathrm{CH_2-C(CH_3)=CH-CH_2}]_n-$ (Isoprene) $\rightarrow$ (Natural Rubber)

2. Chloroprene is 2-chloro-1,3-butadiene. Its polymerization yields a synthetic rubber called neoprene (polychloroprene). $n \, \mathrm{CH_2=C(Cl)-CH=CH_2} \xrightarrow{\text{Polymerization}} -[\mathrm{CH_2-C(Cl)=CH-CH_2}]_n-$ (Chloroprene) $\rightarrow$ (Neoprene)

3. Since natural rubber is a polymer of isoprene, not chloroprene, statement A is incorrect.

Statement B: Teflon is prepared from tetrafluoroethene by heating it with persulphate catalyst at high pressures.

1. Teflon is the trade name for polytetrafluoroethene (PTFE).
2. The monomer for Teflon is tetrafluoroethene ($\mathrm{CF_2=CF_2}$).
3. The polymerization is a free-radical addition polymerization. It is carried out by heating tetrafluoroethene with a free radical initiator, such as a persulphate (e.g., ammonium persulphate, $\mathrm{(NH_4)_2S_2O_8}$) or benzoyl peroxide, under high pressure. $n \, \mathrm{CF_2=CF_2} \xrightarrow{\text{Catalyst, High Pressure}} -[\mathrm{CF_2-CF_2}]_n-$ (Tetrafluoroethene) $\rightarrow$ (Teflon)
4. This statement accurately describes the preparation of Teflon. Therefore, statement B is correct.

Statement C: PVC are thermoplastic polymers.

1. PVC stands for Polyvinyl chloride, with the repeating unit $-[\mathrm{CH_2-CHCl}]_n-$.
2. Thermoplastic polymers are polymers that soften on heating and harden on cooling. They can be remolded repeatedly. This property is due to the fact that they are typically linear or slightly branched polymers where intermolecular forces (like van der Waals forces or dipole-dipole interactions) can be overcome by heat.
3. Thermosetting polymers become hard and infusible on heating due to extensive cross-linking between polymer chains. They cannot be remolded.
4. PVC is a linear polymer. The polar C-Cl bonds create dipole-dipole interactions between the chains. Upon heating, these forces are overcome, allowing the chains to slide past one another, making the material soft and mouldable. It regains its rigidity upon cooling. This is the characteristic behavior of a thermoplastic.
5. Therefore, statement C is correct.

Statement D: Ethene at 350-570 K temperature and 1000-2000 atm pressure in the presence of a peroxide initiator yields high density polythene.

1. There are two main types of polythene (polyethylene):
   • Low-density polythene (LDP): It is prepared by the polymerization of ethene under high pressure (1000-2000 atm) and high temperature (350-570 K) in the presence of a free-radical initiator like dioxygen or a peroxide. The mechanism involves significant chain branching, which prevents the polymer chains from packing closely. This results in a low density and low melting point.
   • High-density polythene (HDP): It is formed when addition polymerization of ethene takes place in a hydrocarbon solvent in the presence of a catalyst such as Ziegler-Natta catalyst (e.g., triethylaluminium and titanium tetrachloride) at a lower temperature (333-343 K) and pressure (6-7 atm). This results in linear polymer chains that can pack closely, leading to a high density and high melting point.
2. The conditions mentioned in the statement (350-570 K, 1000-2000 atm, peroxide initiator) are those for the synthesis of Low-Density Polythene (LDP), not High-Density Polythene (HDP).
3. Therefore, statement D is incorrect.

Conclusion: The correct statements are B and C.