There was the Gold Channel, which was high-priority and real-time. There were other real-time connections made, but they always took some doing, explicitly or implicitly (William Edgars could always call Garibaldi at any moment from Mars, but he was super-rich, while Sheridan and Ivanova had to both pull some strings and wait around to call their respective fathers, and Garibaldi had to go through the Psi Corps office on Mars to get information of Lise when he was checking on her during the riots, since regular channels were unavailable). My read is that there were a finite number of real-time long-range communications channels available to Babylon 5 (and in civilized space in general), and that there were a handful like the Gold Channel that were always kept available for important calls, but for the rest, you had to wait for your turn, not just for Babylon 5's communications to free up, but also whatever relays and whatnot your signal had to pass through to get to whoever you wanted to talk to.
FTL communications don't seem to require a jumpgate (the only time we saw one used that way was when the station was trying to contact a specific ship, but didn't know the location beyond "Somewhere in hyperspace"), so light-speed delay to Jupiter probably isn't a major factor. Bandwidth, however, almost certainly would be. When communications are fuzzy, they always have analog interference, not digital, so if you want to read into that, it could be that interstellar communications doesn't have the speed of our present-day internet, but is stuck in the '90s. As for waiting for search results, a substantial amount of information would be locally cached on Babylon 5, so you'd only need to connect to the central database for really esoteric stuff like, say, detailed crime reports on a series of long-solved murders.
