I have a longer layover in Kula Lumpur (arriving: 07:10, departing: 21:00) so I'd like to visit the Batu Caves.
My planned schedule for that day:
- go to Batu Caves from Kuala Lumpur or directly from the airport
- return to Kuala Lumpur
- lunch/dinner in Kuala Lumpur
- go up Petronas Tower
- return to the airport between 19:00 and 20:00

Is this route doable with the given time schedule (target time for being back from the Batu Caves in Kuala Lumpur: 15:00)?
1.) How long is the travel time to Batu Caves?
2.) Which options do I have to go there? (I'm interested in faster options.)
3.) How long do you recommend to stay at Batu Caves?
4.) Any recommendation for lunch/dinner appreciated (first class cuisine, excellent service, Asian cuisine preferred). The restaurant must open quite early because of my departure time. Lunch/Dinner at ~15:00 would be best.

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