Can I enter time from the Projects screen?

Yes. Open the Overview tab of any project in the detailed view, and click the + icon on the Unbilled Time widget. This opens the Daily Time Card, letting you record time against that project without leaving the screen. Daily Time Card is also accessible from the Top Icon Bar on any CORE screen.

You can also enter time from the Time Entries, Weekly Time Card, or Timers screens under Time & Expenses. When creating a time entry from those screens, you can select the relevant project (and phase) from the drop-down list. You can also quickly access the Time Entries screen from within the project using the Links menu.