Going to answer some of these as I've tested some of this out myself.
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1) Am I right in thinking a large POS can run 15 mobile labs?
It depends on the racial control tower. Caldari would be the way to go for this... it will leave you room for nothing else. (And don't think a POS is safe just becuase it is hi sec!)
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2) Are these labs and subsequent slots available to everyone in system? (I have seen the settings on test server but dont fully understand what does what or if they actually work)
To my knowledge, you can not make the slots publicly available. They are only available to corp mates and alliance mates. This is per settings mind you. Alliance usage has a variety of limitations... well so does corp usage.
Copy Slots: Copies made of T1 bpo's will be delivered into the Mobile Lab it is researched at. For Corp mates this -might- be a problem, for Alliance mates it IS a problem. (Accessibility issues and Trust on both parties)
T2 Research: Major complications as T2 research requires materials. The materials for the research =must= be at the mobile laboratory in question or the research can not be done. This is, as it stands, an impossibility for alliance mates unless you allow open usage of the pos to select alliance mates. (And I haven't tried this out successfully yet!)
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3) Any costs I set on the labs are payable by whoever uses them into my corp/personal wallet? (Ive read conflicting reports on this saying only if in same alliance etc)
Refer to usage allowed.
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4) If someone uses the labs for copying do the copys remain in the station they are in? (I have read that copies appear at POS)
Refer to Copy Slots.
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5) Would any of you pilots out there actually be interested in renting said slots if they were to become available?
Refer to ME Panic Threads all over forums
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6) Where would you reccomend that such a POS was built? (Any empire sytem up to the 0.7 limit is possible)
Unless you are in an alliance that is willing to utilize the facility within the limitations that currently exist.. not really. It's a luxury toy for people with isk to burn. The lab research time "bonus" is very nice indeed... and tempting. But the logistics of running a small personal Mobile lab is manageable whereas running a more grandoise facility can be a proportional challenge.
Hope this helps.
PS: Any one else with some experience in this is free to correct me. Just please give details along with the correction.