When I work out and see that I have more muscle, does that also mean that I have lost some fat? I have visible muscle but also a lot of fat just hanging from my bones.
No. Gaining muscle does not directly equate to losing fat. Case in point; it's possible to gain both at the same time.
What is more likely, is that through gaining muscle, you have lowered your bodyfat percentage. There's more fat, but a smaller percentage of it overall.
It's the bodyfat percentage that mostly dictates muscle visibility and definition.
No, not necessarily, and generally when you're gaining muscle, you're not losing fat. It's very difficult (aside from undergoing puberty or taking steroids/hormones) to gain muscle while losing fat.
However, gaining muscle makes you look better at the same bodyfat percentage. Someone 6'0 who weighs 180 lbs at 20% body fat might have a little pudge on them, but someone at 220 lbs at 20% body fat is going to look significantly more built. This is because the former will have 144 lbs lean mass and 36 lbs fat whereas the latter has 176 lbs lean mass and 44 lbs fat. 8 lbs of fat isn't very much whereas a difference in 32 lbs of lean mass is going to be massive.
The more muscle you have, the more bodyfat you can have on your body before it starts looking "fat."
Usually you gain both at the same time if you eat with a caloric surplus. Most people do this because it's much easier to gain strength and muscle under these conditions, however it is not a prerequisite for muscle gain.
The muscle tonus you are referring to might very well be evidence of increased muscle mass or fat loss. You can also notice more defined muscles if you are dehydrated.