Can I read/write data to the HI 4050 unit over the TCP/IP connection?

Yes, the ability to read/write to the HI 4050 or HI 4060 unit using the TCP/IP connection from a PC is possible.
There are two methods of accessing the data, UDP and TCP.  The UDP methods allows multiple connections to the unit.  The TCP method allows only a single connection.
The UDP and TCP methods are identical as far as what data you send or receive.
The commands are:

PARAMETER ID (to read a parameter value)
Or
PARAMETER ID = VALUE (to set a parameter's value)
Or
<MAPPING SYMBOL> (to read a value from a mapping table)
Or
<MAPPING SYMBOL> = VALUE (to set a value in a mapping table)

All data is ASCII, with the PARAMETER ID in hex, as they are in the parameter dump.  You can find the parameter ID values by accessing the unit through its built in browser and going to "Operations>Diagnostics>Parameters".  On this page you will find the list of parameters with their hex ID number as well as a link at the top of the page for other parameter IDs that are not in the list.  In this list of "other parameter IDs" is the command word (0x0800; mapping symbol HSO2).  This is the parameter ID to use for sending a command like tare, zero, or calibration to the unit.  Each bit within the command word represents a different command.  This bit layout is:
Bit 0 - Tare
Bit 1 - Zero
Bit 2 - Hard Cal Low
Bit 3 - Hard Cal High
Bit 4 - C2 Cal
Bit 5 - Save to SD card
Bit 6 - Print
Bit 7 - Clear Tare
Bit 8 - Midpoint Cal (hard cal)
Bit 9 - Disable Midpoint Cal
Bit 10 - Start Check Weigh Zero measurement
Bit 11 - Clear Check Weigh Tamper
Bits 12-15 currently unused

Mapping symbols can be found on the Mapping page "Configuration>Mapping" in the drop down lists, or on this page there is a link for a list of mapping symbols.

The commands should be framed with a starting linefeed character and an ending carriage return, as for example: