Learn English – Using “among others” for a list of workplaces

First and foremost, it should be noted that news[paper] headlines are usually not useful examples of valid grammatical constructions. Having said that, OP's example...

Bomb explosion hit Magallanes City, killed 7 and 9 others wounded.

...is a particularly egregious construction (I think it's truly awful). Very likely the writer wasn't what I would call a native Anglophone in the first place. The reason it's so bad is that killed and wounded are effectively being used as different "parts of speech" (the first is closer to a verb: the bomb killed 7, but the second looks more like an adjectival past participle: 9 were wounded [by the bomb]).

Having said that, I don't see much point in ELL discussing how headlines could be better phrased. OP's suggested alternative probably is "better", but with an article (probably A) in front, it would never be considered "grammatical" in normal speech/writing.

OP's notion that the subject of the sentence must not be the doer of the action in the past participle phrase might have some relevance in this exact construction, but there's nothing wrong with any of...

A bomb explosion that hit Magallanes, killing 7 and wounding 9 others, was terrorist-inspired.
and
A bomb explosion that hit Magallanes and killed 7 and wounded 9 others, was terrorist-inspired.
or
The bomb that killed the US ambassador to Libya was terrorist-inspired.
and
The bomb that exploded in Benghazi, killing the US ambassador to Libya, was terrorist-inspired.

At risk is a prepositional phrase, in which risk is a figurative location. You are at risk when you are in a continual state of risking some sort of harm. (English likes to conceptualize abstract states as locations, each with its obligatory preposition: in danger, in love, on cloud nine, under the weather, ... please suggest more examples in the comments.)

Adding a hyphen, at-risk, transforms the phrase into an adjective, meaning "the modified noun has the property of being at risk". You can use hyphens this way with any prepositional phrase. For instance, suppose you have

Jane McFamousPerson's fans in Los Angeles were excited to attend her public Q&A session last Thursday ...

you can turn that into

Jane McFamousPerson's in-Los-Angeles fans were excited ...

with basically the same meaning. However, it is unusual to do this with "ordinary" prepositional phrases. At-risk gets used this way a lot because it's neutral -- it expresses no judgment on how the group at risk got to be that way. That's important when you're an NGO trying to help people. So it is preferred to more colorful terms (e.g. impoverished) which, in English, often carry a weight of moral disapproval.