Hi, interesting questions -
there is of course the soca database which is based on ecoinvent and thus reflecting products, but the main social LCA databases are based in IO databases that use money terms for all economic flows that link processes. This is not a limitation though. When you make a social LCA model, you should have a foreground system, based on products, and you can link this foreground system with a social LCA background database by setting a price for each product that is input in your foreground system. So e.g. if you have an input of 15 kWh electricity, you determine the price per product amount for this, and link this to an energy generation sector in the social LCA database.
This way you will not have a different result if you have an input product in 1g or 1kg as the price will reflect this change of amount.
This maybe answers your first two bullet points. Regarding the question of the combined model, this is possible with soca (if you are fine with the limitations - the extent for social LCA is somewhat reduced compared to e.g. PSILCA since the models are much smaller and do not contain services and only a small section of the overall economy).
Best wishes,
Andreas