First time backing up Hard drive questions

Hard drive started making questionable noises a couple days ago. Have an external hard drive lying around so decided to back everything up on it in case anything went haywire. But I've never had to deal with backing stuff up and/or moving it as it's still the same hard drive that's been in my PC since I built it so I have a couple questions for anyone willing to throw advice my way.

First, if the drive does fail at any given moment and I have everything backed up to my external, can I restore everything to a new hard drive once I get one? I've gotten mixed responses on this.

If I get a second hard drive and put it in, can I transfer everything from the old to the new without buying special software for it? Been thinking about upgrading anyway so now may as well be the time, but again never had to do it before so I'm not too sure how to go about it.

And if yes to either of the two above, HOW do I go about it? I know this stuff is probably second nature to most people here and it may sound dumb but it would be great to help a noob out :3

Thanks in advance.

the first question can be answered with a simple. yes. and you would go about it exactly how you would think you would.

the second one im not sureĀ 

I figured but keep getting people telling me it isn't that simple or some other reason.

Well if that's the case I should hopefully be safe then.

Another question while I'm thinking about it. There is about 540gb worth of stuff on my 1TB hard drive. On my external which is also 1TB and solely used for backup, it's up to 867gb. Is there a reason it's so much larger than my hard drive? It's backing up once a week and it's almost out of room already o.O