I lost a scarf in synagogue some weeks ago, there are now three identical scarves hanging in the cloakroom, without obvious simonim, can I assume one is mine and take it?

If the scarves are identical to the one you lost and they have been in the cloakroom for a while, you can take one of them on the assumption it is yours. Even if the scarves were not identical, just so similar that it is likely that whoever took yours left his by mistake, you can take it after waiting enough time to give the fellow who took your scarf a chance to realize his mistake and correct it. The assumption is that the person who made the mistake would prefer this arrangement to any other (Pitchei Choshen Hilchot Aveida ch. 4, p.292).