yes you can and should wear your regimental tie.
normaly worn with a regiment crested navy sport coat and grey dress pants.
i wear mine to legion functions and with medals to rememberance day parade.
remember, if you honourable served a regiment, you are always going to be part of that unit.
Nope, don't and never did to my knowledge. The British guards officers wore bowler hats and carried brollies, as did officers from Oz but not Canadians.
At one time regimental scarves were popular with blue blazer and often with uniforms such as Bush jackets and BD tunics. French Blue for the PPCLI, for example, and black, gold and blue stripes for the RCR.
British Guards officers and also members of the Household Cavalry still wear bowler hats and carry rolled brollies (never to be unrolled!), with dark suits and regimental tie, as witness a recent photo of Princes Harry and William that appeared in the press. I think the same also applies to other cavalry regiments.