In premier league games, The referee is supposed to report on the performance of his assistants back to the board - 'word of mouth' holds a lot of sway (we can't inspect everybody, every week), and this feedback can affect future reports.
Assuming the appointments haven't changed since first drawn up, the first grade ref is a board member anyway - and the young AR in question is a first year ref....or possibly a 2nd year ref.
Why are such referees given roles on the lines in PL? Maybe nobody else was available, or maybe somebody else had given positive feedback. While a single bad decision may not be enough to affect future appointments - after all, we've all missed blatant offsides or other infringements (we're only human after all), if he generally wasn't confident, then that should be provided in the feedback. If the ref's assessor wasn't in line for the offside, then he might not be sure if it was missed anyway - you can't tell a damn thing with offsides when you're further down the pitch, and a player who looks 10 yards off may well be 5 yards on.
So yes, performance will (well, should - assuming the feedback is actually provided) will affect future performances.
As for 'jurisdiction on the field' - well, basically the AR has to figure out if the ref had a good view, or if the AR had a better view. If he thinks the ref had a clear view, then he should leave it - so sometimes, even right in front, the ref may have a clear view and the AR will leave it - although usually the closer to the AR, the more the ref will depend on the AR for the foul, unless he feels like he's had a decent view, or he thinks the AR has left it to him. Teamwork between refs is tricky, and it's a tough balance to get right.
Often on the line I've had offences happen some 40-50m away, and spectators asking me why I didn't flag. That far away, it's certainly within the referee's jurisdiction, and if the ref hasn't called it it's probably because his angle said something different. From that distance, the AR would only call it if he's adamant that the ref has missed something due to his angle (very, very rare case - normally you'd just assume the ref's view was better), or if the ref was looking over to you for help. 9/10 if the AR flags for something that's happened more within the refs 'territory', he's just interfering.
And then it comes down to confidence - it can take years for a young AR to develop the confidence to call fouls from the line. That's fair enough, and I always tell them the best place to start is calling the real blatant ones the ref's going to call anyway, then you can build up to calling the things the ref's missed. Really, the ref should find out the AR's confidence level before the match and take that into account.
As for throw-ins, AR's are generally told that if the ref signals first, just go with him even if you disagree. That's why, when the AR has a better view, the ref should hesitate first. If the ref's signalled straight away, then the AR's just supposed to agree, not offer a different opinion.
Then sometimes you just know you've got the kind of ref who isn't going to listen to you anyway, so why bother...