Analyzing each statement:
1 CO₂ is most acidic among group 14 dioxides - correct, it's a non-metal acidic oxide.
2 Carbon shows negative oxidation states (-4 in methane, -3 in ethane, etc.) along with +2 and +4 - correct.
3 Carbon covalency cannot exceed 4 - correct, as it's period 2 element unable to expand octet.
4 ¹³C is radioactive - incorrect. ¹³C is a stable, non-radioactive isotope. ¹⁴C is the radioactive isotope used in radiocarbon dating with half-life of 5730 years. Therefore, statement (4) is incorrect.