NuGet do I need to install Microsoft.EntityFrameworkCore if all I need is its provider?

If you are referencing a package via PackageReference, you automatically get all of it's dependencies as well.

Microsoft.EntityFrameworkCore.Sqlite 3.0.0 (targeting .NETStandard 2.1) depends on Microsoft.EntityFrameworkCore.Sqlite.Core 3.0.0, which depends on Microsoft.EntityFrameworkCore.Relational 3.0.0, which eventually depends on Microsoft.EntityFrameworkCore 3.0.0 (which now further depends on other packages).

So a PackageReference of

<Project>
  <ItemGroup>
    <PackageReference Include="Microsoft.EntityFrameworkCore.Sqlite" Version="3.0.0" />
  </ItemGroup>
</Project>

gets your project not only the top-level package, but also all transitive dependencies as dependency graph - if the PackageReferences of those projects in return isn't tagged with PrivateAssets to prevent the flow to the parent project, as described in the docs.

You can review all the assemblies consumed by your project via the Solution Explorer of Visual Studio:

Or alternatively via the .NET Core CLI by typing: dotnet list package --include-transitive

Project 'Project' has the following package references
   [netcoreapp3.0]:
   Top-level Package                           Requested   Resolved
   > Microsoft.EntityFrameworkCore.Sqlite      3.0.0       3.0.0

   Transitive Package                                           Resolved
   > Microsoft.Data.Sqlite.Core                                 3.0.0
   > Microsoft.DotNet.PlatformAbstractions                      3.0.0
   > Microsoft.EntityFrameworkCore                              3.0.0
   > Microsoft.EntityFrameworkCore.Abstractions                 3.0.0
   > Microsoft.EntityFrameworkCore.Analyzers                    3.0.0
   > Microsoft.EntityFrameworkCore.Relational                   3.0.0
   > Microsoft.EntityFrameworkCore.Sqlite.Core                  3.0.0
   > Microsoft.Extensions.Caching.Abstractions                  3.0.0
   > Microsoft.Extensions.Caching.Memory                        3.0.0
   > Microsoft.Extensions.Configuration                         3.0.0
   > Microsoft.Extensions.Configuration.Abstractions            3.0.0
   > Microsoft.Extensions.Configuration.Binder                  3.0.0
   > Microsoft.Extensions.DependencyInjection                   3.0.0
   > Microsoft.Extensions.DependencyInjection.Abstractions      3.0.0
   > Microsoft.Extensions.DependencyModel                       3.0.0
   > Microsoft.Extensions.Logging                               3.0.0
   > Microsoft.Extensions.Logging.Abstractions                  3.0.0
   > Microsoft.Extensions.Options                               3.0.0
   > Microsoft.Extensions.Primitives                            3.0.0
   > SQLitePCLRaw.bundle_e_sqlite3                              2.0.0
   > SQLitePCLRaw.core                                          2.0.0
   > SQLitePCLRaw.lib.e_sqlite3                                 2.0.0
   > SQLitePCLRaw.provider.dynamic_cdecl                        2.0.0
   > System.Collections.Immutable                               1.6.0
   > System.ComponentModel.Annotations                          4.6.0
   > System.Diagnostics.DiagnosticSource                        4.6.0
   > System.Memory                                              4.5.3
   > System.Text.Json                                           4.6.0
   > System.Threading.Tasks.Extensions                          4.5.2

To answer your second question: You may want to just install Microsoft.EntityFrameworkCore for database provider agnostic class libraries, providing general Entity Framework Core functionality.