No, not all Themes accommodate all features; but to answer that question more precisely, you’ll need to be more specific about what you consider to be “features”.
Things that are generally considered Theme features are fairly well-represented by the list of filter tags for WORG repository-hosted Themes. You’ll notice that these things generally deal with presentation of content.
Things dealing with creation or management of content are generally considered Plugin territory, and generally speaking, any Theme should accommodate such Plugins.
(Your second question is unrelated, and should be asked in a separate question.)