So for example if my lillipup used tail whip then would it lower the defence more than if my oshawott used it (lillipup=normal oshawott=water)
No. Only ATTACKING moves can receive STAB. Lillipup's Tackle would do more than Oshawott's Tackle.
No they don't.
The only moves that get Same Type Attack Bonus are attacking moves.
No, Status Moves do not get STAB at all. So if a Lillipup and Oshawott use Tail Whip, they will both lower Defense by 1 stage regardless of the Stat.
No only damage moves that dont have a set damage get stab.
As for tail whip its def would be lowered by 1 stage and always would be unless they had the ability contrary.