That is a lot of questions, let me try to address them one by one:
I was wondering if anyone knows what frequency (frequencies),
effective radiated power (ERP), and the modulation modes (I am
assuming it's PCM) are being used
There has been little in the public domain in regards to the on-board RF equipment of the Falcon-Heavy, and it is assumed no RF equipment on the Tesla (e.g. it is using 2nd stage infrastructure).
From a related question & answer the frequencies of the Falcon-9 are well documented, including their Pout in dBm, purpose, and modulation, the following from newer (Rev-2) version of the Falcon-9 user-guide:
Whether they actually used PCM modulation is not certain. The older Falcon-9 (Rev-1) user-guide actually lists NTSC as a feed protocol for Stage-2 Video, Page 37, Table 5.2:
The newer (Rev-2) version of the Falcon-9 user-guide does not list this type of table, nor does in mentions NTSC at all.
Are they using the TDRSS satellites for data relay (although the data
is only high definition images, no usable telemetry metrics that I
They are not, the just over 4-hour live feed came from the Stage-2 directly, until batteries ran out (8-hours sooner than expected)
I have been watching for any signs of data loss (dropouts) and so far
this is still a very strong signal from the "spacecraft". I saw no
drop outs as it performed its barbecue continuous yaw thermal control
maneuver about its axis; I looked all over the SpaceX website, but
there is very little technical information.
Unfortunately the live-feed has ceased due to battery depleation. The only video's left on the internet are re-runs of the first 4 hours. Although you can find lots of references that the video ran out after 4 hours, none of them are authoratitive. Most of them are news outlets, with various levels of trustworthyness.
However SpaceX own website has an article which clearly details the following:
"You can watch a replay of the test flight below, as well as a replay of the live view of Starman in orbit"
One may safely assume there is no longer a live feed, when the best SpaceX themselves have; is a replay.
It would appear that the only antennae are omnidirectional - no sign
of a parabolic dish, or X-Y drives for positioning it.
It is not sure what type of antennas, omnidirectional or directional, are on the Falcon-Heavy. Again referencing an older Rev-1 Falcon-9 user-guide Page 11, does show us the design for that launch vehicle:
Again, it is logical to assume that the Falcon-Heavy is similar than the Falcon-9 in this regard.
Without actual details in the public domain on the Falcon-Heavy, this answer is unfortunately based on quite some assumptions. Nevertheless, it will give you a good idea how communications could have been handled.