batters interference/interference by teammate

[_Bruno_]

1.
R3, 1-1 count, 0 outs, wild pitch.
R3 takes off for home. the catcher quickley gets to the backstop, picks up the ball and fires to homeplate. the batter is standing at homeplate and signals the runner to get down and gets hit by the throw (unintentionally) which prevents the pitcher from making the play at R3. i called R3 out due to the batters interference. but was it really interference ? i ruled that the batter could have easily avoided by beeing hit by the throw.

what if the batter and pitcher made contact (unintentionally) during the throw ? interference ?
what if the batter and pitcher made contact (unintentionally) without a play ? (catcher was still chasing the ball)

2.
R1, 1-1 count, 0 outs, wild pitch.
R1 takes off for 2ndbase. the catcher, a very fast guy, runs to the backstop, picks the ball up, and fires to 2ndbase, but the batter interferes with the throw (standing at homeplate, could easily avoid the throw).
who's out ?
batter interfered, the throw did not retire the runner immediately : Batter out, R1 back to 1B ?
or
the batter is treated as an offensive teammate and so R1 is out ?