I often use virtual instruments and software synthesizers on my computer with my PSR-E models-- the YPT-400 (which is the PSR-E403 with a different name for export purposes), the PSR-E433, the PSR-E443, and the PSR-EW400. I haven't used a hardware MIDI sound module with them, but I've used one to play another (i.e., a "master keyboard" and "slave keyboard" configuration), as well as to play the MX49 BK, so it's more or less the same as using a MIDI sound module-- the only difference being that I'm not directly connecting a PSR-E keyboard to another MIDI device, but am using a computer to route the MIDI between them.
If you want to play a MIDI sound module with your PSR-E443 using a direct connection (i.e., without needing to use a computer as a go-between), you're going to need an additional piece of hardware known as a "MIDI USB host interface," or something similar-- the name varies a bit from company to company. This is due to the fact that the PSR-E443 doesn't have MIDI DIN ports, only a USB TO HOST port, and if you want to connect two devices together via USB then one of them must serve as a host device for the other one.
Note that you cannot simply use a USB-to-MIDI adapter cable, because those types of cables are for connecting a device with MIDI DIN ports to a USB host, and the PSR-E443 can't act as a USB host in that situation. (It can act as a USB host for a USB flash drive, but not for a MIDI device.)
Instead, you'll need something like a
Kenton MIDI USB Host, or a
Sevilla Soft USB Host MIDI Router, or maybe one of the
iConnectivity MIDI interfaces that can act as a USB host. (If you do decide to get an iConnectivity MIDI interface, make sure it's one that has both types of USB ports, A and B-- namely, the mio10, mio4, or iConnectMIDI4+.) There are a couple of other companies that make MIDI USB host interfaces, so you might want to search for "MIDI USB host" to see what your choices are.
The other option is to connect your PSR-E443 to your computer, connect the other MIDI device to your computer, and use computer software to route the MIDI data between your PSR-E443 and the other MIDI device. I normally use a DAW for this, because a DAW can function as a MIDI router, MIDI event filter, MIDI event processor, and MIDI sequencer, as well as a host for virtual instruments, not to mention as an audio and MIDI recorder, editor, and mixer. But you can also use something as simple as MIDI-OX.
As for latency, it's usually caused by the computer's audio processing. That isn't the only source of latency-- any electrical or electronic signal needs to travel over wires or through circuits, so there will always be some latency as the signal goes from point A to point B-- but usually latency is so small that you don't notice it. However, computers are designed to perform many different tasks at the same time, and even if you aren't running any other programs besides your DAW there are still all sorts of processes running in the background. Therefore when a program transmits an audio signal to the computer's sound card, the signal doesn't necessarily get sent to the sound card right away, because the computer's processor might have several other things to do first, which introduces latency. Also, computers will typically collect data in a buffer before sending it on, so the buffering process also introduces latency.
But there are ways to reduce that latency. If your computer has a sound card that can use ASIO or something similar, that can help reduce the latency. Note that if you don't have a sound card that can use ASIO, there is a free program called ASIO4ALL that basically imitates or emulates ASIO. And another way you can reduce the latency is to decrease the size of the audio buffer so the audio data doesn't get held back as much while the computer waits for the buffer to fill up. By using ASIO4ALL (or ASIO if you can), and decreasing the audio buffer size, you should be able to reduce the latency to be more or less unnoticeable.