What you might find most easy is to make a portable installation of the Arduino IDE on a computer that does have the necessary network access, install everything you need via Boards Manager on that computer, and then copy the full installation over to the locked down computer (you can even just leave the portable installation on some portable storage such as flash drive if that is convenient).
Information about the Arduino IDE portable installation option here:
But I'll go ahead and provide answers to your questions as well:
If you know the "Boards Manager URL" (package index), you can find it in there. The authors of modern 3rd party boards packages will always tell you the URL in their installation instructions because you must add it to the Arduino IDE preferences. The primary package index URL is hardcoded into the Arduino IDE, so it is not so well advertised. It is here:
https://downloads.arduino.cc/packages/package_index.json
Here is the package index entry for version 1.8.2 of the "Arduino SAMD Boards (32-bits ARM Cortex-M0+)" boards platform:
{
"name": "Arduino SAMD Boards (32-bits ARM Cortex-M0+)",
"architecture": "samd",
"version": "1.8.2",
"category": "Arduino",
"help": {
"online": "http://www.arduino.cc/en/Reference/HomePage"
},
"url": "http://downloads.arduino.cc/cores/samd-1.8.2.tar.bz2",
"archiveFileName": "samd-1.8.2.tar.bz2",
"checksum": "SHA-256:af75e0d37b63df3b92ecca60285aa59bab66e0bd03bcc4092ea3a1fab3df5258",
"size": "2894202",
"boards": [
{ "name": "Arduino MKR WiFi 1010" },
{ "name": "Arduino Zero" },
{ "name": "Arduino MKR1000" },
{ "name": "Arduino MKRZERO" },
{ "name": "Arduino MKR FOX 1200" },
{ "name": "Arduino MKR WAN 1300" },
{ "name": "Arduino MKR GSM 1400" },
{ "name": "Arduino MKR NB 1500" },
{ "name": "Arduino MKR Vidor 4000" },
{ "name": "Arduino Nano 33 IoT" },
{ "name": "Arduino M0 Pro" },
{ "name": "Arduino M0" },
{ "name": "Arduino Tian" },
{ "name": "Adafruit Circuit Playground Express" }
],
"toolsDependencies": [
{
"packager": "arduino",
"name": "arm-none-eabi-gcc",
"version": "7-2017q4"
},
{
"packager": "arduino",
"name": "bossac",
"version": "1.7.0-arduino3"
},
{
"packager": "arduino",
"name": "openocd",
"version": "0.10.0-arduino7"
},
{
"packager": "arduino",
"name": "CMSIS",
"version": "4.5.0"
},
{
"packager": "arduino",
"name": "CMSIS-Atmel",
"version": "1.2.0"
},
{
"packager": "arduino",
"name": "arduinoOTA",
"version": "1.2.1"
}
]
}
You can get the platform archive download URL from the packages[*].platforms[*].url field (in this case, http://downloads.arduino.cc/cores/samd-1.8.2.tar.bz2).
Note that the platform is only one component of the package. You also need the toolchain. The platform's tool dependencies are listed in the packages[*].platforms[*].toolsDependencies[*] fields. Their archive URLs are also listed in the package index. For example, here is arduino:arm-none-eabi-gcc@7-2017q4:
{
"name": "arm-none-eabi-gcc",
"version": "7-2017q4",
"systems": [
{
"host": "arm-linux-gnueabihf",
"url": "http://downloads.arduino.cc/tools/gcc-arm-none-eabi-7-2019-q4-major-linuxarm.tar.bz2",
"archiveFileName": "gcc-arm-none-eabi-7-2019-q4-major-linuxarm.tar.bz2",
"checksum": "SHA-256:34180943d95f759c66444a40b032f7dd9159a562670fc334f049567de140c51b",
"size": "96613739"
},
{
"host": "aarch64-linux-gnu",
"url": "http://downloads.arduino.cc/tools/gcc-arm-none-eabi-7-2018-q2-update-linuxarm64.tar.bz2",
"archiveFileName": "gcc-arm-none-eabi-7-2018-q2-update-linuxarm64.tar.bz2",
"checksum": "SHA-256:6fb5752fb4d11012bd0a1ceb93a19d0641ff7cf29d289b3e6b86b99768e66f76",
"size": "99558726"
},
{
"host": "i686-mingw32",
"url": "http://downloads.arduino.cc/tools/gcc-arm-none-eabi-7-2017-q4-major-win32-arduino1.zip",
"archiveFileName": "gcc-arm-none-eabi-7-2017-q4-major-win32-arduino1.zip",
"checksum": "SHA-256:96dd0091856f4d2eb21046eba571321feecf7d50b9c156f708b2a8b683903382",
"size": "131761924"
},
{
"host": "x86_64-apple-darwin",
"url": "http://downloads.arduino.cc/tools/gcc-arm-none-eabi-7-2017-q4-major-mac.tar.bz2",
"archiveFileName": "gcc-arm-none-eabi-7-2017-q4-major-mac.tar.bz2",
"checksum": "SHA-256:89b776c7cf0591c810b5b60067e4dc113b5b71bc50084a536e71b894a97fdccb",
"size": "104550003"
},
{
"host": "x86_64-pc-linux-gnu",
"url": "http://downloads.arduino.cc/tools/gcc-arm-none-eabi-7-2017-q4-major-linux64.tar.bz2",
"archiveFileName": "gcc-arm-none-eabi-7-2017-q4-major-linux64.tar.bz2",
"checksum": "SHA-256:96a029e2ae130a1210eaa69e309ea40463028eab18ba19c1086e4c2dafe69a6a",
"size": "99857645"
},
{
"host": "i686-pc-linux-gnu",
"url": "http://downloads.arduino.cc/tools/gcc-arm-none-eabi-7-2018-q2-update-linux32.tar.bz2",
"archiveFileName": "gcc-arm-none-eabi-7-2018-q2-update-linux32.tar.bz2",
"checksum": "SHA-256:090a0bc2b1956bc49392dff924a6c30fa57c88130097b1972204d67a45ce3cf3",
"size": "97427309"
}
]
}
Note that there is a separate URL for each host type, so make sure to get the right one for the PC you are installing to.
It is also possible for package index authors to reference a tool dependency from another package, so you won't necessarily always find the tool in the same package index as the platform. The referenced tool is usually from the arduino package, in which case you would find it in the https://downloads.arduino.cc/packages/package_index.json package index.
In the unlikely event you are interested in all the boring details about package indexes, you can find them here:
https://arduino.github.io/arduino-cli/latest/package_index_json-specification/
Yeah, you can install them manually. People usually manually install platforms to the hardware subfolder of their sketchbook because they are most often doing beta testing and development and that location is more convenient for such activities. This installation option is described in the introduction of the Arduino Platform Specification:
https://arduino.github.io/arduino-cli/latest/platform-specification/
Unfortunately, there isn't any provision for installing tools to the sketchbook folder. It is usually most convenient to do an installation of the production release of a platform to get the associated toolchain, then install the development version of that platform to the sketchbook. But in your case I suppose the Boards Manager option is off the table.