Hello Gerjo,
As first a high-level answer to your question, LabVIEW would be perfect for this type of application. This is presuming that all your sensors are generating a voltage as their output, as this is the most straight-forward type of signal to measure with LabVIEW and data acquisition hardware. The most difficult part of the requirements to meet would probably be the weight requirement.
As for a brief response to your direct questions:
1) Yes, the most basic solution would use LabVIEW and DAQ hardware. Depending on the response time needs of the application, you might need the Real-Time module as well, but I'm not sure that it would be necessary.
2) Personally I have very little knowledge of the sensors market, sorry.
3) Probably a PCMCIA-bas
ed DAQ card if Real-Time is not needed. If Real-Time is needed, your lightest weight option would be a FP-20xx with the necessary input modules.
4) Cost, as well as the exact hardware once known, would be something better to discuss with a NI sales representative, or you can check out the "Products & Services" section of NI's web site for a good price estimite.
5) Again, a laptop might be the lightest option, alternatively FieldPoint hardware might meet your weight requirements as well.
6) Depending on the exact calculations you need to do and whether or not LabVIEW has VIs already built to do them (for many it does, make sure you get the Full or Professional development system, not the Base package) you likely will not need to know much about the "conventional" methods you speak of.
I hope this helps. One other note, if your requirements are for a deterministic control system, you are definitely in the right place. If you think code running on a Windows computer would b
e sufficient, I would strongly suggest posting your original question to the general LabVIEW group as it would get a larger audience there.