Refactor to remove late variables + clean up cyclic dependencies

[eliasyishak]

We should limit/remove instances of late and late final variables within classes since there may be usage patterns that we have not anticipated that could cause late initialization errors.

Referenced in this issue:

• Fix late initialization error for Analytics.userProperty #239 (comment)

PRs with changes to remove late and late final:

• Fix session handler file: Limit writes to session file #243
• Fix AnalyticsImpl: Refactoring to remove late variables and cyclic dependencies #247