10 days in South of Italy - Advice needed :)

Dear Readers,

I was thinking to go to South of Italy for 10days. I'd like to have some advices regarding my itinerary.

1st day
12.15 - Arrive in Naples' Airport, take the ANM bus to Piazza Garibaldi then go to Stazione Centrale for lunch.
I'm going to try the best pizza in Naples, at Da Michele near Stazione Centrale.
After having lunch, go to Pompeii with Circumvesuviana Train.
18.00 - Arrive in Pompeii, stay over here.

2nd day
Explore Pompeii. Go to the Vesuvius Mountain. It was written in LP that there is only one transport to go up, which is with Vesuviana Mobilita in Piazza Anfiteatro. Is there any other public transport to get to that mountain?
17.00 - Head to Positino : go to Sorrento with Circumvesuvania Train then take the SITA bus nearby.
18.30 - Arrive in Positino, stay over here.

3rd day
I would like to do the Path of the Gods. Could you help me where can i get the walking map?
I prefer to do it on my own than take a guide. Is it easy to be explored on my own?

4th day
Visit Grotta dello Smerlado.

5th day
09.00 - Head to Matera: go to Salerno with SITA bus. In Salerno train station, take bus/train to Ferrandina and continue with another bus to Matera.
15.00 - Arrive in Matera, stay over here.

6th day
Explore Matera.
Is it possible to go to the parco of Rupestrian Churces without a guide?

7th day
08.00 - Head to Grotta di Castella: go to Bari with train then continue with Bari - Taranto line.
11.00 - Arrive in the train station, take a bus to the Grotta.
15.00 - Head to Alberobello: take the Bari - Taranto line.
17.00 - Arrive in Alberobello, stay over here.

8th day.
Explore Alberobello.
Could you suggest me an one day trip itinerary around this place?

9th day.
14.00 - Head to Rome: go to Bari with the train and go to the airport.
18.46 - Leave Bari to Rome.
19.45 - Arrive in Rome, stay over here.

10th day.
Explore Rome.
Night flight to Jakarta.

That's all.
I hope you could give me some advices.
Thank you in advance.

Regards,
Christina.

Edited by: utinepunya