Can it be asked a long term assignment ?
Older editions (1-3) note: nature spirits only lasted until the next sunrise or sunset, so for them the answer would be no. There isn't a set time I can find for elementals, but based on my answer for #2 I'd say there should probably be a pretty limited time period (maybe days=force would be fair?). It's also worth noting that an elemental that was more than a certain distance from the summoner would go free after completing it's current service.
Can he be bound to an item and be summoned back ?
There aren't rules for this that I'm aware of.
However, there are rules for binding elementals to guard a certain site. It cost karma equal to the force of the elemental and lasted for a year and a day. I'd say it's a sufficiently similar situation, personally.
All that said, if it's an NPC, just do what you like. The idea is not distinctly un-Shadowrun, and there's no rule that PCs should be able to do or even understand everything an NPC can do.