Looks like you glanced over one of the errors:
Package "@ngtools/webpack" has an incompatible peer dependency to "typescript" (requires ">=3.4 < 3.6", would install "3.7.5").
Try a lower version of @ngtools/webpack that works with TypeScript 3.4 to 3.5.
Alternatively, update your TypeScript version in the package.json to 3.7.5 and run npm update, then you should be able to update @angular/core & @angular/cli.