Haven't flown on AC for a long time, last time I was on A340 without PTV. I'm flying from YQB to FRA with YYZ as a long stopover (in J), which is around 7h, can I...

(1) check bag through to FRA from YQB?
(2) do my carry-on bag fit on CRJ900 bin (its a Rimowa 16in x 16in x 8in)? if not and gated checked, can I check my bag only to YYZ?
(3) use Signature Suite for the whole duration of stopover? as the flight is sold as LX codeshare, but it is not a reward flight

Thanks!