Are some traits in children inherited solely from one parent and the rest from the other or are traits a blend of both parents?

Yes to both. Genetics is an amazing field and there is new information everyday. There are some physical traits that are inherited from one or both parents. There are some things that are traceable to one parent. There are also traits that are environmentally passed on...Many behavior traits are actually observed and learned that way. If you have a specific "trait" in mind asking a geneticist will be best.
A complex blend. The personality is like a jigsaw puzzle. Traits don't exist separately but come together to form the whole child.. Occasionally one trait may stand out but usually you see traits influencing one another whether they are inherited or come from the environment.