I don't know if calling in will get you the routing you want, but it's worth a try. I know there are some partners that you can't book online, only by calling in.
With regard to your luggage, yes. You can through check across multiple tickets so long as the
operating carrier is a tier 1 carrier.
As for IRROPS, truly depends. They're not obligated to protect you. However, in my experience you'd have a good chance of being fine. I would expect them to rebook you on a later flight regardless of which carrier caused the delay and which ticket was affected. That said, this would only be the case if the various flights and tickets were T1 partners and not someone else. I think if you were to fly LAX-CDG on AF (not sure who flies this route) and then on to AF to NCE they'd just put you on the next flight to NCE should you miss it. Similar with a flight to TLV, depending on your routing and carriers involved.
I've nested tickets like this numerous times and so far haven't run into problems. (Knock on wood)