A number of social media websites, including Facebook, will auto-resize and compress your images to conform to that given site's standards. This may result in an undesirable compression or size. A site such as Flickr provides greater user-definable size and compression controls, including the original full size image for sharing, should you wish.
Batch processing is possible by recording actions or using programs such as Bridge, Lightroom or Aperture. Consult the manuals of these programs if it is likely you'll be undertaking considerable name and size edits frequently.
Outside of ‘social media' there are online-hosting sites, such as Photoshop.com and others that provide large amounts of space for a subscription fee. These archives aren't as ‘open' as social media websites, allowing for more peer-to-peer sharing of images, even interactive editing in some cases.
If the smaller version of your image doesn't look as crisp and sharp as the original, then look into sharpening. Photoshop's ‘Unsharp Mask' feature will find edges within the image and amplify them for a sharper appearance.
Rather than sending multiple files in an email (and slowly attaching each), and as it's not possible to send a folder, multiple files may be ‘zipped' together. WinZip, WinRar or StuffIt are common examples of such programs. Email attachments are usually returned as undelivered if greater than 10MB.