[The Best Apps You've Never Heard of] DiamondJohn:
I understand you are looking for a FREE launcher, but with the launcher being so integral to your device experience, maybe thats the one app you should be prepared to pay for.

I have been using what I think is the most powerful and customizable launcher. Not only does it do the few things you mentioned:

Put any icon on any grid (or no grid at all), and,

Save a backup file of the homescreen to load onto any other device

Note that this backup file includes all installed apps in the location that they are installed in - which - for me - is important since EVERY app icon is placed in an EXACT location for a reason.

Place a widget INSIDE any folder on the homescreen (yes thats launcher specific)

So it does ALL what you listed (i know its a quick list), but also (among many MANY other things..)

Folders inside folders, inside folders.... and widgets n deep in the folder structure

Any widget can be Resized, Scaled (Different to resize which I think is more on the widget to resize itself), Rotated, transparency, Skewed (think parallelogram), positioned to a decimal pixel position

All visible (or even hidden transparent hot-spots) have complete control of the event (eg start ab app, start a script etc) or I *thinik* even multiple actions (I dont use that feature)

All items covered by 3 above also have short AND long press events (Tap, Long Tap, Swipe Left, Swipe Right, Swipe up, Swipe down) I personally have transparent hot-spots (on top of other widgets that respond to their default tap), that I swipe uy[p on to turn on AUID and down to turn off AOD. I also have a long press on my navigation, which turns on GPS, Bluetooth (to connect and call handsfree), starts my music player, starts playing the music and finally starts the Navigation app ready to navigate.

Lots of visual effects such as shadow of the text

Control of the Font, Size, position/offset

"Reflections" on the icons, as if they are hovering above a crystal clear pool/puddle of water

You can have/add code to make your own things. There is an example out there how to add a analogue clock simply with code. Well beyond any of my needs.

and on and on and on...

My personal experience is, if you can imagine it, then there is a way to do it. I have been using it since gingerbread, and as I upgrade device and/or ROMs, I use the backup / restore to get the launcher config started. NB: The private widget data/config doesn't come across in the launcher backup, but a "fallback" image/placeholder is show, reminding you of how you previously had it set up. So although there is a steep learning curve, and with ALL the different options/function can take some time to set up how you want, a lot will transfer onto your next device or ROM. But since its a paid app, you can only run it on one device at a time.

Now, the thing to REALLY take note of, the default set-up on first install is utter TOTAL rubbish ,and so are the preview/demo images on the PlayStore. It really is a case of "if you can imagine it, you can do it"

Oh, and the launcher is called "Lightening Launcher Extreme"

The following are some screen shots I qui8ckly snapped, but the actual config is of course very personal. And because its so customizable, I can do things others will hate ;) I just quickly flashed through the screens I personally use the most in set-up, but didn't scroll through anything or ensured I got everything that is beyond the screen and there are many more options/features I dont use; or even know about.