[Gareth D]

attacking player receives the ball whilst straddling the half way line (one leg in own half, other leg in opponents half)

Offiside or not ???

Ten minutes later, same pass to the same attacker, both legs in own half but upper body and one arm in opponents half,

Offside or not ???
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Rustington FC - The Blues !!!

[Thunderer]

Firstly, I assume none of the defending team are in their own half of the pitch. Secondly, the ball has been played by another attacking player from within their own half.
In the first part, as one foot is in the oppositon half of the field, when the ball was played him, then he is offside.
In the second part, if any part of his body, which can legally play the ball, ie chest or head, is in the opponents half, then again he is offside.
If however, it was just his arm, which cannot legally play the ball, then he would not be penalised.