My cousin got one just like this and i asked her a bunch of questions so of course i will help^^.
You can PM me for more info^^
to heal...: initial healing of a tattoo is about 5 to 10 days, complete healing of a tattoo is 45 days, this is how long it takes for skin to regenerate itself after being damaged.
as for the cost..i didnt really ask her but i know that probably around $100+tip. most shops have a shop minimum they charge that costs anywhere from $40-$50.
I hope this was very useful to you^-^