Can せる be added to a any verb to convey what someone can do?

In the module I've stumbled upon this sentence.
えいご　を　はなせる　ひと　は　います　か

Here  はなす has been changed to はなせる to mean "someone who can speak". 

How does this verb ending せる apply to other words? 

Could I say for example:　スーさんはりょうりせるいます。
Sue is a person who can cook? 


 

Nope.

seru is actually the causative. Meaning making someone do something.

In your earlier example, the seru is a potential form. Someone is able to do something.

Ryouri is a noun so it can't take seru, it can take suru koto ga dekiru, form of structure.

Note that no and koto makes verbs into nouns.

So
Ryouri o suru no ga tanoshii, cooking is fun
Ryouri o suru koto ga muzukashiku nai, it isn't hard to cook.

With the verb you could use seru/reru

Hanaseru> able to speak
Hashireru> able to run
tabereru> able to eat. mase will be: taberemasu extended form: taberu koto ga dekiru/masu.

The causative and passive is for advanced students. Better to keep that for last.