#1
So I just put Beefys on my guitar. Tuned to standard D/Drop C. It didn't seem to affect my intonation, and make the action better because now there is no buzz.. but.. if I continue to use these strings (pretty sure that I am) do I need to adjust my truss rod or will it be okay even playing in standard D? Mind you, I used to use 10-46 strings.
#2
You should be fine, the strings have more tension but your also in a lower tuning so that means less tension. Not running tens in Standard E tuning Might cause issues over time.

The truss rod always needs to be checked with any tuning change or string gauge change or even periodically even if no changes were made to the guitar.... So yes that might need to be adjusted..