Yes. Radiation does count as splash damage according to the Borderlands wikia:
"Radiation has been added as a replacement/adaptation of the explosive element from previous installments, which now finds itself as splash damage, rather than its own element."
It's discussed further on this Reddit post where users discuss and accept using Radiation as a primary element for a Moze build. There's a similar discussion on the Gearbox forums too.
In regards to your second question of Aura Boost: there is another post on Reddit which makes the same inquiry.
Reddit user u/GreenDragon245 performs some tests:
"It does not boost the red suit shield tested this with a lvl 31 red suit the 1 that says warning containment failure I believe just to make sure.
Tested this with no rad boost just the shield 145dmg per pulse when near enemies equipped a similar relic with aura dmg+50% and aura burst dmg and burst radius both 12% still 145 per pulse. Even with a different relic that grant's a aura when u slam I had a rad one two different rad dmg values showed up 145 and 200 something so ya that's your answer.
Oh 1 more my guardian ranks were locked when I tried this so iam sure it does not boost the red suit
What the relic says is it boosts radiation when a enemies is infected with radiation it has a aura remember? Lol that dmg harms other things nearby now the relic makes since
One final test I did was with moze nuclear warheads on her mech on a vehicle see if it boosted the dmg no it did not 918 and 63ish rad tick dmg with it on and off"
"In conclusion it does not boost radiation dmg directly but the aura it projects is more deadly."