Essentially, I have a fraternity mug, which is unique and specific to me, that sustained a hairline fracture. I was making tea, and not having anything else to put hot water into, I put some water into the mug. I then noticed it leaking and discovered a small hairline crack that ran from the bottom to near the top of the mug. I'm pretty certain the heat from the water caused this.
1)sorry to tell you unless you have the original glaze to re-glaze over the crack it is unrepairable. Even that method may make it worse by spreading the crack out. You must be careful when using pottery or ceramics after they have a crack due to bacterial that can now grow in the crack. Use it as a small planter for a small plant for your desk that way you'll have it to remind you.
2)you can use mseal which is the best way but do apply outside and not inside
though u fell it wont look niec or it may spoil ur mug
since it is an hairline crack use a small amount which wont look dirty