The similarity is described by the minimum number of letters you have to add, remove or replace in order to get from the entered word to one of the dictionary.

Mathematically, this is a well-defined measure with no ambiguity. minimum is the keyword here - it does not matter which changes you make to go from one string to the other, as long as you do as few as possible. This problem is well-known and there are existing algorithms to solve it that you can readily find online.

You beated it in an hour, I'm here 9 hours and yet cannot solve it

Boggle is not a method, it's a constructor of the class under test. I guess you are supposed to set up your solution in the constructor, and perform actual search in Check. I do not know if this design is really necessary for such task, but since it was authored like this, you need to stick to it.

What language?

Yes, kata says that dot is 1 time unit long and dash is 3 time units long, but it does not say how many 1s are in single time unit: is it 1, or 11 or 111 or 1111. On the contrary, it explicitly says that time unit can differ between test cases:

However, the standard does not specify how long that "time unit" is. And in fact different operators would transmit at different speed.
Function [...] should find out the transmission rate of the message...

Your task is to find out, for every test case, how many 1s and 0s are in one time unit.

Transmission rate differs from test to test. In one test case E can be 11, and in another test case it can be 111. It's your task to find out what it is in given test case.

Also remember about this reuirement: "[...] if you have trouble discerning if the particular sequence of 1's is a dot or a dash, assume it's a dot."