The LDCM and RDCM messages are likely battery related. Low battery or bad battery or loose or corroded battery connections.
The TCS codes could be the result of a bad EBCM or they could also be corroded connections or grounds.
Here's a thread with some info about C1243 worth reading.
For code C1233 I'd pull the wheel, separate the connector to the wheel speed sensor and look at the condition of the contacts. I'll bet that on a 2000 year C5 they are corroded or damaged. I'd also check the connectors on the other 3 wheels while I was at it.
For the C1277 code, have you cleared this code and does it return???? htere is plenty of reading if you do an extended search co C1277 in both title and text . Could be a battery issue, could be a ground at the EBCM, could be a ground at the PCM or could be a damaged wire at the EBCM or it could be a bad EBCM.
Given the commonality of grounds for the TCS codes you have, Id read the Bill Curlee thread about grounds and spend some time cleaning the many that are on the car: