How do you record multiple synthesizers?
If your synths support USB midi then you only need to plug USB cables from your synths to your computer to record midi, to record audio you'll need to plug the line outs of your synths into an audio interface, and if you have more synths than inputs on your audio interface you'll need a mixer.
How do you sync synths together?
One way to link your synths together is by daisy-chaining them together via MIDI connection. This is a practice electric guitarists will be familiar with, as the process is much the same as that of daisy-chaining pedals together on your effects pedalboard.