The compilation warnings that you are getting are because VersionOne.SDK.APIClient is currently using internally V1APIconnector, and this warnings are only shown because, I guess, you are including VersionOne.SDK.APIClient inside your project, this approach is, sometimes, not advisable because you may miss updates. The best thing to do should be to use nuget. Add to VS a reference (Tools -> Options -> Packate Manager -> Package Sources) to V1 gallery on myget.org (https://www.myget.org/F/versionone/), in this way you'll have your DLLs updated.
Regarding your questions: There's no need for you to directly use VersionOneAPIConnector, but here you have two examples of listing child projects: one using Metamodel as you mention that you were using, and another using VersionOneAPIConnector.
//Example 1: Listing all child projects of 'Foo' with MetaModel
var assetType = _context.MetaModel.GetAssetType("Scope");
var query = new Query(assetType);
//Filter Attribute
var parentNameAttribute = assetType.GetAttributeDefinition("Parent.Name");
//Filter
var filter = new FilterTerm(parentNameAttribute);
filter.Equal("Foo");
query.Filter = filter;
var result = _context.Services.Retrieve(query);
Example 2: Listing all child projects of 'Foo' with VersionOneAPIConnector and V1 user and password.
Stream streamResult = new VersionOneAPIConnector("https://abc.org/v1sdktesting/rest-1.v1/Data/Scope?where=Parent.Name=%27Foo%27").WithVersionOneUsernameAndPassword("usr","pwd").GetData();