TPS65000's PGND and AGND

Please find answers embedded below.

1. Should I directly connect PGND with AGND in my circuit?

Yes AGND and PGND should be connected, typ. we recommend the to have a single point connection of AGND, PGND (star point).

This connection point should be as close as possible to the IC.

2. [Analog ground - Star back to PGND as close to the IC as possible.] <-- what is the note mean?

   It is hard to me to understand  what is “Star back to PGND as close to the IC as possible”

See above, there should be a single point connection between AGND( e.g. feedback divider reference GND) and PGND (GND connection for high current paths LDO & DC/DC inputs and outputs) 

3. TSP65000 has only Thermal Pad. How can I connect PGND to PowerPAD?

You are correct the TPS65000 has an exposed thermal pad. The exposed thermal pad needs to be connetced to GND plane to provide good thermal performance of the device. Typ. the exposed thermal pad is connected with via to the PGND plane on your PCB.

Please have a look at the TPS65000EVM-469 layout for guidance on the GND scheme connection.

Here is the link to the TPS65000EVM-469 User's Guide http://focus.ti.com/general/docs/lit/getliterature.tsp?literatureNumber=slvu293&fileType=pdf

4. Should I connect Thermal PAD to PGND?

Yes this is recommended to provide good thermal performance of the device. The exposed thermal pad should be connected to a copper plane.

As mentioned above please have a look at the TPS65000EVM-469 for guidance.