R not installing properly in default folders (Corrupted/Improper Installation)

Does anyone here have advanced experience in R/Rstudio installation script and can help debug some very weird behavior?

Right now...
C:/Users/studentsname/DOCUMENTS/R/R-4.0.2/bin/x64 <-for the literal installation of R itself. Instead of the following.
C:/Program Files/R/R-4.0.2

Q: How could someone install R to the wrong default directory? Or change it?

Q: In general some of these settings make no sense about the R studio setup. What does Rstudio get from the windows system to decide these values?

COMPAT_LAYER DetectorsAppHealth
ALLUSERSPROFILE C:\ProgramData
APPDATA C:\Users\username\AppData\Roaming
CLICOLOR_FORCE 1 Common\ProgramFiles
C:\Program Files\Common Files
CommonProgramFiles(x86)
C:\Program Files (x86)\Common Files
CommonProgramW6432
C:\Program Files\Common Files
COMPUTERNAME acomputer
ComSpec C:\windows\system32\cmd.exe
DISPLAY :0
DriverData C:\Windows\System32\Drivers\DriverData
FPS_BROWSER_APP_PROFILE_STRING Internet Explorer
FPS_BROWSER_USER_PROFILE_STRING Default
GFORTRAN_STDERR_UNIT -1
GFORTRAN_STDOUT_UNIT -1
HOME C:\Users\username\Documents
HOMEDRIVE H:
HOMEPATH *
HOMESHARE \isiloncifs\Home
LOCALAPPDATA C:\Users\username\AppData\Local
LOGONSERVER \VDC1DCTL2
MPLENGINE tkAgg
MSYS2_ENV_CONV_EXC R_ARCH
NUMBER_OF_PROCESSORS 4
OneDrive C:\Users\Administrator\OneDrive
OS Windows_NT
PATH C:\Users\username\Documents\R\R-4.0.2\bin\x64;
C:\Program Files (x86)\Common Files\Oracle\Java\javapath;
C:\windows\system32;
C:\windows;
C:\windows\System32\Wbem;
C:\windows\System32\WindowsPowerShell\v1.0;
C:\windows\System32\OpenSSH;
C:\Program Files (x86)\Enterprise Vault\EVClient;
C:\Users\username\AppData\Local\Microsoft\WindowsApps;
C:\Users\username\AppData\Local\GitHubDesktop\bin
PATHEXT .COM;.EXE;.BAT;.CMD;.VBS;.VBE;.JS;.JSE;.WSF;.WSH;.MSC
PROCESSOR_ARCHITECTURE
AMD64
PROCESSOR_IDENTIFIER
Intel64 Family 6 Model 78
Stepping 3, GenuineIntel PROCESSOR_LEVEL
6
PROCESSOR_REVISION 4e03
PRODUCT_CONF C:\ProgramData\CTES\Components\DARAgent\home\product.conf
ProgramData C:\ProgramData
ProgramFiles C:\Program Files
ProgramFiles(x86)C:\Program Files (x86)
ProgramW6432 C:\Program Files
PSModulePath C:\Program Files\WindowsPowerShell\Modules;
C:\windows\system32\WindowsPowerShell\v1.0\Modules
PUBLIC C:\Users\Public
QT_D3DCREATE_MULTITHREADED
1
R_ARCH /x64
R_COMPILED_BY gcc 8.3.0
R_DOC_DIR C:/Users/username/DOCUME~1/R/R-40~1.2/doc
R_HOME C:/Users/username/DOCUME~1/R/R-40~1.2
R_LIBS_USER C:/Users/username/Documents/R/win-library/4.0
R_USER C:/Users/username/Documents
RMARKDOWN_MATHJAX_PATH
C:/Program
Files/RStudio/resources/mathjax-27
RS_LOCAL_PEER \.\pipe\33789-rsession
RS_RPOSTBACK_PATH C:/Program Files/RStudio/bin/rpostback
RS_SHARED_SECRET 63341846741
RSTUDIO 1
RSTUDIO_CONSOLE_COLOR 256
RSTUDIO_CONSOLE_WIDTH 80
RSTUDIO_MSYS_SSH C:/Program Files/RStudio/bin/msys-ssh-1000-18
RSTUDIO_PANDOC C:/Program Files/RStudio/bin/pandoc
STUDIO_PROGRAM_MODE desktop
RSTUDIO_SESSION_PORT 33789
RSTUDIO_USER_IDENTITY username
RSTUDIO_WINUTILS C:/Program Files/RStudio/bin/winutils
SESSIONNAME Console
SystemDrive C:
SystemRoot C:\windows
TEMP C:\Users\username\AppData\Local\Temp
TERM xterm-256color
TMP C:\Users\username\AppData\Local\Temp
UATDATA C:\windows\CCM\UATData\D9F8C395
****************
USERDNSDOMAIN ***********
USERDOMAIN ***********
USERDOMAIN_ROAMINGPROFILE ***********
USERNAME username
USERPROFILE C:\Users\username
windir C:\windows