In communication with interplanetary space probes, it is clear that one has to take the delay caused by speed of light into account. Besides that, what are current limits for the data upload and download bitrates? What is the main cause of the limit?
Speed-of-light delay is mostly irrelevant for data transmission rates. Once you get out of Earth orbit, transmissions are generally "fire and forget"; if data gets garbled, you schedule a retransmission of the garbled portion at a later time.
The limit for interplanetary communication rates is the Shannon limit: how fast you can send data while still being able to distinguish it from background noise. This in turn is influenced by antenna gain (a bigger sending or receiving dish lets you transmit faster), transmission power (a "louder" transmitter can send data faster), and distance (the further apart your antennas are, the more the signal fades towards background levels and the slower you can transmit).
Because of how many variables there are, there is no one "achievable bitrate". I wouldn't be surprised to find that Arecibo could talk to a counterpart in Neptune orbit at gigabit or even terabit data rates, while the Galileo probe's non-directional antenna could talk to the Deep Space Network antennas at only 160 bits per second from Jupiter.
If you want to see what sort of data rates are in real-world use, NASA's Deep Space Network status page will show you which probes are currently transmitting or receiving, and if you select "more details", it will tell you the transmission rate (for example, as I write this, antenna 15 at Goldstone is receiving data from MRO at 1.5 Mbps).
Spacecraft do not communicate using either TCP or UDP. These are both Internet Protocol applications used in terrestrial networks such as the Internet and private internal networks. They were developed as part of the IEEE 802 internet standards following the Open Systems Interconnect (OSI) conceptual design.
NASA and other national space agencies use technologies based on the Space Communications and Navigation (SCaN) Data Standard Project. This was in turn created by the Consultative Committee for Space Data Systems, of which NASA is one of 11 member agencies.
Instead of TCP/IP, spacecraft use protocols classified as things such as MOIMS (Mission Ops & Information Management Systems), SOIS (Spacecraft Onboard Interface Services), SIS (Space Internetworking Services), and SLS (Space Link Services) to name a few. More specifics can be found here: https://www.nasa.gov/directorates/heo/scan/engineering/datastandards/index.html