Do you not have building regs approval for this job?

If you have, the drawings will show what is required.

Why do you need to support the new floor joists on the old concrete floor, the joists should go into the walls of the building (with new 'joist seals' fitted)

If mid-span support is needed (a vented sleeper wall) then presumably the old outer wall of the lean-to wold be adequate for this?  Only a site inspection can determine whether this is adequate though.

What's going on the 'oversite' of the new bit?  i.e. the additional 2.5 metres past the old lean-to.

Joists will need a 175mm air gap under them.

On ground floor suspended floors, insulation is placed between the (treated) joists, NOT under them.

Your regs approved drawings will show what insulation the council require, usually 130mm Celotex or equivalent.