How do I format my external hard disk to make it compatible with mac? Also, once I Format, will the hard disk still work with windows?

1. Reformat it as Mac OS Extended (Journaled), or if you still need to use it on a PC(outside of a network share), MS-DOS, FAT32 or exFAT. Reformatting it will erase everything on it.

2. See #1.

(109806)

See this link:

Format external drives to Mac OS Extended before using with Aperture

http://support.apple.com/kb/HT3509

MacOS Extended is the only format, that is supported for Aperture libraries. You cannot use a drive, that hosts an Aperture library, with a Windows system. So if you want to use the drive for Aperture or iPhoto, partition it and create one partition that is compatible with your PC software. But on no account move your Aperture library onto a MS-DOS, FAT32 or exFAT partition (iPhoto: Issues with FAT32-formatted drives).

But after formatting how will I get back my data because its in a windows laptop. So after formatting will it still work with windows?

No, see the edits to my post.

It might be best, to buy an additional drive for your Aperture library.

You need to copy all data, you need to save, to a backup drive, before you format your drive, and after that, you cannot read it from a Windows PC:

The reason, that Aperture and iPhoto need MAcOS Extended formatted drives, is, that an Aperture library is a database system, that references internal files, and the pathnames require the MacOS Extended filesystem. Storing the library on a different system may cause database corruption and dataloss.

Connect windows formatted hard disk to macbook on one side with USB and connect another mac formatted hard disk to other USB port and copy-paste files from one hard disk to another?

Yes, you can connect your external drive formatted for Windows to one USB port of the MacBook Air and another drive formatted MacOS Extended, and then drag and drop files and folders from one drive to the other using the Finder. You don't need to copy and paste.

Also, so when I go for buying an external hard disk compatible with mac, what should I ask the shopkeeper exactly? (the technical specifications I mean)

To use the disk with your MAcBook Air you will probably want a small drive, that is not hard to carry around with your MacBook Air. I'd try to get a small 1 TB drive, that will give you plenty of room for your photos of videos.

Check the connections, that your MacBook Air has. or Aperture you will want to have the fastest connection possible. Does your MacBook Air have a Thunderbolt port or USB 3? Both are very fast connections. If your Mac has these ports, get a drive with Thunderbolt or USB 3 connection.

So I will ask for hard disk with Thunderbolt or USB 3 Connection with 1 TB size? Nothing else right?

That should do. You don't need a drive with fancy backup software preinstalled or preformatted for Mac. Do the formatting yourself with Disk Utility as described in the link I gave above:

Format external drives to Mac OS Extended before using with Aperture

http://support.apple.com/kb/HT3509