Amira, the base looks fine. It was probably planted more deeply before, that part was covered by its soil mix. No problem. Like Stefan says, I doubt this is M. albilanata.

Darn. I guess it comes with the Ebay territory. So more likely a rebutia? I will have to look up the care information. Thank you both.

Not more likely, but possible. Mammilaria has tubercules:

http://www.cactus-art.biz/note-book/Dictionary/Dictionary_T/dictionary_tubercle.htm

https://en.wikipedia.org/wiki/Tubercle

While rebutia has those, they are vastly shorter, and more integrated into the cactus stem(they dont poke out as much as those on mammilaria, and there arent gaps between them.

Im saying its possible it could be a rebutia because i cant see the gapped tubercules on the photos, but you can...

The flowers will tell. Mammillaria have flowers near the top, Rebutia flowers come from near the soil line. Care for both is the same, don’t worry about that.

Will keep an eye out for any flowers then and post photos.

Am sad that it isn't a albilanata, will have to keep searching for one.