Is it possible to carry out a radius search within a city(lat&lon)?
The most efficient search is usually a bounding box (so just return the results within this box) but we do also have lat/lon options for searching up to a distance from a point, or polygon searches where you provide an (simplified) encoded polyline for the polygon of the area you are interested in.
We don’t provide a filter on city, if you look at results within your target area you will see many of the city fields are empty or may not be consistently populated as it’s just text. You could return results using a bounding box then filter the results client side on specific “city” keywords.
Is it possible that sometimes locations within the bounding box are not found, but are found in a radius search for a specific lat/long?
If your possible search results exceeded the default max results then you will not see all possible results, so for instance a bounding box query with maxresults=10 will show 10 results in order of their appearance in our spatial index. I think a lat/lon query would be in order for nearest distance to the point.