TST/API: Simplify testing functions API
Derived from #10507. Consider better API for testing functions.
### 1. How to specify comparison tolerance

Current assert functions have `check_less_precise` and `check_exact` flags to specify how to compare values:
- `check_exact=True`: Use `assert_equal`, comparison using `==`.
- `check_exact=False` and `check_less_precise=False`: Use `assert_almost_equal`, comparing 5 digits after decimal points (default)
- `check_exact=False` and `check_less_precise=True`: Use `assert_almost_equal`, comparing 3 digits after decimal points

There can be single kw to specify above behaviors?
### 2. Make integrated assert  function

I think it's nice to have test functions which supports all `pandas` objects for users who is starting contribution / using pandas as their dependencies. Changing `assertEquals` and `assertAlmostEquals` to internally use current `assert_index/series/frame_equal` is one idea.
### 3. Remove `assert_almost_equal`

Remove `assert_almost_equal` and use class-based validation method. Also add input type validation to `numpy_assert_array_equal`.

xref #9895.
