I had a similar problem, where RStudio does not recognize my network drive, but when I look a the Windows 10 File explore, I notice a red X over the drive name. When I try to open the drive (using windows file explore) the X is removed and after that everything works as normal.
If that doesn't work, go to Tools > Global options > General. What R version are you using? Make sure it is the one you just installed into "Documents".
Next. If you want to upgrade R. do that in in an R console, not RStudio. You have to navigate the correct installation as you mentioned is in Documents, an start the correct R executable there. First install installR, then use that to install/upgrade R and RTools as well. Until you get everything running install everything using the R console with R Studio closed.
Next try using the actual network address not your mapped drive address. That might work as well.