Can Shimano Claris R2000 shifters be paired with Claris 2400 derailleurs? Can I use the modern looking shifters with the older model derailleurs without any problems in shifting?
Yes, you can use any 8 or 9 speed rear derailleur (with the traditional cable pull ratio, but SRAM 1:1 does not matter here) with 8 speed shifters. The same for the front ones. That includes these two Claris generations.
Your combination is compatible.