A puzzle is not an excuse for having a guess-author-intention kata.

• triangular numbers instead of triangle numbers / triange numbers / tri numbers

• Description is not well formatted

• Lacks novelty thooo

Do read this FYI https://docs.codewars.com/authoring/kata/create-first-kata/#kata-idea-and-duplicates

• Sample tests are incorrect: test.assert_equals(royalfam(100), 20000) should be test.assert_equals(royalfam(100), "00")
• Solutions with forbidden characters pass
• I got '2' should equal '02' and '08' should equal '8'

From the kata description:

• You are to calculate the LAST two digits of this number
• You should return a string

Yet the sample tests are like this:

test.assert_equals(royalfam(100), 20000)

There shouldn't be two #1 of the same series.

• Solutions with *, %, pow pass the tests.

• Sample tests don't work.

I think you are trying to increase the difficulty the wrong way. All you have done is prepend a very basic string matching problem (8-7k) to your previous kata (7k).
The two tasks feel completely unrelated, and completing two 7kyu problems in a row is barely harder than solving one (definitely not 5k!). If anything, the difficulty only comes from understanding the kata in the first place.
If you want to make this an increasingly difficult series of puzzles that follow the same theme, why not add requirements that suit the theme?

Ideas off the top of my head:

• Require function to handle all 'dimensions' (ie. in dim 3, n*2 and n/2 are both cubic numbers) def royalfam(n, d)
• Provided a list of numbers, return the 'odd one out' (ie. only one that is in royalfam, or only one that is not)

Those are still pretty easy but I hope they convey what I mean.

The link to the previous kata is wrong.

Don't add code-length restriction just because you don't want people to write long solutions.

There's no reason to have 2,000 tests.

The description's format needs to be fixed

Still a duplicate.

Expected results are wrong (floating point errors).

Floats are compared for strict equality.