Export image in Apple Photos

1. For the most part yes, though any format that is different to the original file will have some compression and loss so will not be 100% 1 to 1. But for all intents and purposes it will be pretty much the same image.

If you need exactly the original file and all its embedded information without any sort of compression or quality loss then you need to use the "Export Unmodified Original" option from the File Menu.

2. No. You get a TIFF image. But you will not gain any quality from doing that. It will retain whatever image quality the original jpeg had which is a fairly lossy format to begin with.

If you export with the settings shown in this screenshot you'll get a jpeg file that is greater than the original.

You will be hard pressed to see any difference between it and the original unless you've made some dramatic edits like cropping, removing items, changing exposure.

The High JPEG Quality setting give you a file close to the unedited original.

I started with a 36 MB 100% jpg image from a Lightroom RAW edit, cropped it in Photos, and then blew it up 2000% from there. I compared a TIFF export (6MB), a jpg Max export (1.5MB), and the Lightroom jpg. The export sizes represent lots of cropping, not loss of quality. Pixels were pretty big! But I didn't see any real difference. Here is some blue sky next to an Eagle's head:

I thought the blue sky would be most susceptible to compression. I'm not sure how this survives the web upload, but, really, they look the same. The Eagle's eyelash looks the same, as well.

The TIFF export is 4 times as big, but looks the same as the 100% jpg. I'm not sure what the point of using TIFF would be…