I have ridden the Catherine-de-Barnes stretch recently on my commute to work. That was before the recent rain, so a little out of date. It was OK on an upwrong, with a couple of muddy patches by Damson Road. It gets quite narrow in parts, so a trike might struggle. Between Lode Lane (near JLR) and C-de-B there are two barriers to stop motorbikes. These would be an issue with a trike if you struggle to lift it. Once you get past JLR you'll be fine. Solihull renovated the towpath 20 years ago, but appear to have done nothing since. Once you get to Acock's Green, Birmingham City Council have spent money on the towpath and it seems good, although I haven't ridden into Brum for ages. IIRC, a couple of the humpback bridges have brick bumps which would be uncomfortable on a trike.
If you want a route to bypass the canal until Lode Lane from C-de-B, I'd ride up Hampton Lane towards Solihull, turn right onto Damson Parkway for a short stretch, turn left onto Yew Tree Lane (which becomes Cornyx Lane, then becomes Moat Lane), then turn right onto Lode Lane. There is a cyclepath of sorts that will take you to just before JLR. The GU is then accessible by a path - with steps! - but you will avoid the narrower bits of the towpath and the worst of any mud.
Architecturally, the original(?) Solihull bridges are intact, but often have newer bits of road added on to them. At Dovehouse Lane they left the old bridge intact and built a new bridge. You'll also notice dates imprinted into the concrete edgings. These are 1933/4 when this stretch of the canal was widened during the depression. Should you need shops, Richmond Road bridge has (awkward) access and there is a row of shops and a cafe. Not much in the way of food shopping though, but there's a newsagent. Not sure about Sunday hours.