You don't need to use syslinux. The installer for Slackware64-14.2 will propose you to use elilo instead, and that generally works. Answer "yes" to both questions "Install elilo" and "Install a boot menu entry". It won't hurt to install lilo also, if your machine is able to boot in Legacy mode.
To be proposed to use elilo as boot loader by the installer you need to:
- Install Slackware64-14.2 (64-bit)
- Make sure that you machine is set up to boot either in UEFI mode or if in both mode with priority UEFI.
If case of issue come back: we will try to help.
PS it is true that the elilo project has stalled, but this should not bother you: in your use case it should just work.
PS2 To answer your last questions: during installation and after the TARGET step your root partition will be mounted as /mnt and you will be able to access it from another virtual terminal pressing Alt+F2. Alt+F1 will get you back to the installer.
Anyway at end of installation you are now asked if you want to reboot. If you say No (probably because you need to perform some task before rebooting) you are dropped to a shell an can do what you want, including chrooting to your new installation.
In in any case the installer will never install a boot loader against your will. This hasn't changed for years (decades?) and comes handy for people who for instance prefer to update the boot loader's configuration of another distribution already installed.
Caveat: I have no experience myself with NVMe.