There is a bit of a difference. Advice is more personal, like what you might give to someone who is having relationship problems. A suggestion is more impersonal, for example what you might give to someone who needs help with a presentation. It's a really subtle difference though, and in most circumstances they're interchangeable.
As for when to use advice as singular or plural, "advice" is both singular and plural, so you don't need to worry about it.