Don't know what to suggest about your muted-audio issue.

But as far as installing Win7 to M.2 PCIe NVMe which doesn't work (vs. installing Win7 to 2.5" SATA3 SSD which works fine), the problem has been discussed at length on the Internet (as you already know).

This issue first concerns Skylake chipset, and support for USB being in the Embedded Controller of the P70 BIOS which requires special USB/EC drivers in order to support USB mouse/keyboard which of course is required to perform a Windows installation. Support for USB/EC is not contained in the default Win7 installer from Microsoft from 8 years ago.  It is present in the Win10 installer.

Similarly, driver support for installing to PCIe NVMe target device is again not present in the 8-year old Win7 installer, while again it is present in the Win10 installer.

So, all manufacturers of Skylake motherboards who support Win7 have faced this issue for their customer base, Lenovo included. There are several similar "solutions" available which revolve around rebuilding new bootable USB Win7 install media where the required missing drivers for USB/EC as well as for NVMe target device are "slipstreamed" into the install media.  This will enable you to then install Win7 to a Skylake target machine (e.g. P70) and have full support for USB mouse/keyboard as well as installing to an NVMe target drive.

There are several threads on this laptop forum (as well as on the desktop forum) directly related to this issue as it pertains to Lenovo Skylake-based P50/P70 laptops as well as Lenovo Skylake-based M700/M800/M900 desktops.  For example this one discusses installing Win7 to a P50.  Mention is made of the utility available from Gigabyte which can rebuild new bootable USB install media for Win7 that includes the missing drivers.  The utility is available from the Gigabyte download site for "Utility", i.e. the item named "Windows USB Installation Tool to Support Intel 100 series motherboards" and will also add the missing NVMe drivers.

On the desktop side, here's a forum article discussing the same problem for wanting to downgrade an M900 to Win7, and not having the proper drivers, and using the same Gigabyte solution to overcome the problem of the missing USB/EC and NVMe drivers.

The Windows 7 installation with the Gigabyte tool worked very fine, but i have the same problem like before with the Sound.

Regarding your speaker issue...

The following story regarding my P70 took place over some time, but conceptually it occurred as follows: (with no problem with sound, either from speakers or from headphone jack):

I have a P70 that came with Win7 pre-installed by Lenovo, to HDD spinner.  I installed my own two purchased M.2 Samsung 950 Pro NVMe drives, and then installed Samsung NVMe Controller driver into the pre-installed Win7, so that the two new NVMe drives could now be seen while stlll running from Win7.  This is critical and mandatory since MS's Win7 does not support NVMe natively as Win10 does.  I also installed Samsung Magician, which doesn't do as much for NVMe as it does for SATA3, but at least it still supports "over-provisioning" which I planned to use.

Then I used Macrium Reflect (running under the pre-installed Win7) to "clone" Win7 from the HDD spinner directly over to NVMe0, reducing the size of the Win7 partition on NVMe0 such that sufficient unallocated space on NVMe0 was left to support both (a) Samsung Magician "over-provisioning", which needs about 10% of the drive, as well as (b) two additional non-C data partitions on NVMe0, as well as (c) an 85GB area I was going to use to install Win10 (retail, from scratch, using OEM license key in the UEFI BIOS of my P70) as a second bootable Windows (along with the Lenovo-provided Win7) available through Boot Manager on my P70.

Then I rebooted, got into BIOS Setup utility, changed the boot drive sequence so that NVMe0 was right after USB HDD and optical CD/DVD, saved and re-booted.  Confirmed that I was now booted to the cloned Win7 as C, running from NVMe0 950 Pro.  I then ran Partition Wizard Free and created several data partitions on the second 950 Pro in NVMe1.  I then deleted all factory-provided partitions on the original Lenovo HDD spinner and used Partition Wizard to create additional new "data" partitions on the HDD spinner.

Eventually I replaced the 2.5" SATA3 Lenovo HDD spinner with a 2.5" SATA3 Samsung 850 Pro SSD, partitioned identically to the Lenovo HDD spinner it replaced.  So now I was running all-SSD (2.5" 850 Pro drive and two M.2 950 Pro NVMe drives).

After things settled down and I was satisfied with my P70 customization and all of my 3rd-party software installs into the cloned Lenovo-provided Win7, I then installed Win10 into that 85GB space I'd reserved for it on NVMe0.  The Win10 installer added Win10 to the Boot Manager menu as expected, now allowing me to run either Lenovo's pre-installed Win7 or my own from-scratch installed Win10, both from NVMe0.

Ok... audio on the P70.  No problems whatsoever either from Win7 or Win10, no matter using speakers or headphone jack.

In Win7 I'm using the Lenovo-provided Realtek audio driver 6.0.1.7746 from February (this is the version which finally solved the "pop/crack" speaker noise issue that had plagued early delivered models of P50/P70 for several months).  I had been using the same driver version for Win10 but now notice that Lenovo has just last week released 6.0.1.7898, which I have not yet applied.

I also have the Hotkeys Integration software installed in both Win7 and Win10, to provide onscreen display for audio-related functions when using the audio-related keyboard keys.

There are two sets of keys on the P70 keyboard which pertain to audio: Fn+F1=mute, Fn+F2=volume down, Fn+F3=volume up, along with the matching set of audio-only keys at the top of the numeric keypad on the right side of the keyboard.  The "mute" LED is in the mute key over the numeric pad.  For me, everything works fine both in Win7 and Win10, with the expected volume adjustments occurring though both speakers and headphones when using either set of keys.

All of the onscreen displays corresponding to using the audio-related keys also work properly, both in Win7 and Win10.

Sounds like everything except the actual speakers on your P70 is working the same as it should, including audio from the headphone jack and resulting audio level changes from using your audio-related keys.  The only problem is that you have ZERO SOUND from the speakers.

I am going to speculate you have a defective P70, related to choosing "speakers".  I don't know about the hardware enough to know if this is in the Realtek chip itself, or if there's a separate amplifier for the speakers, or what.  But if you bought your P70 "retail"/new it's obviously still under warranty.

I'd suggest contacting Lenovo to open a support ticket.  Depending on what support options (if any) you also purchased they will either come to your home and swap whatever part(s) they need to (perhaps a new motherboard is the only solution), or you will need to bring/send your P70 to a service center for repair and return to you.

I don't think you've done anything wrong software-wise.  Sounds like a real hardware issue.

Note that there are three BIOS-related settings (Config -> Keyboard) which in some way affect how the F1-F12 keys work as far as audio (and other functions) is concerned.  But these BIOS settings don't affect the operation or behavior of the audio-only keys at the top of the numeric keypad on the right side of the keyboard.  And besides, it really just seems the amplifier/speakers are broken, as everything is working just fine through heapdhone jack.

Nevertheless, you might at least try playing with the F1-F12 primary/Fn BIOS setting, to see if that makes any difference at all (which I don't think it will).

So, I just had the same problem with my laptop. But I found the soultion. The speaker light was on despite the fact that the volume was at 100%. So, I tried the basics of reinstalling drivers and restarting and as far as the windows troubbleshooter was concerned, everything was fine. So I started to think a little, I ajusted the screen brightness before the problems using the fn keys. I remember hitting the wrong key before I hit f5. I hit f1 (The Fn key to mute audio) and the mute light came off and it worked fine after that. So that is the soultion I found and just want to help. 

Holy sht, thank you! Just bought a p70 and had the same issue. What an odd decision that the fn mute completely overrides and blocks the numpad mute. Thanks anyway, you saved me a lot of driver shenanigans!