In the UK by outside and overtake, we mean on the off-side.
The other way, the nearside/curbside/inside can be a more dangerous place, but it is still do-able with care.
Just be really careful about getting doored and crossing junctions on the inside through stopped traffic. You do not have right of way on the main road over a turning vehicle if the traffic is stopped. You do if you ride on the offside, but on the nearside, according to several (US) court cases, you have to yield.
Cyclists dont need a whole lane to themselves, so can pass standing cars in the gaps between lanes. There is nothing illegal about that. I get cars passing me in the gap between my vehicle and the other lane.