Clarification on interpolation techniques in pandas

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Python

DataFrame

data-science

I want to experiment with different interpolation techniques. Some determining factors for choosing the appropriate interpolation techniques are:

1. Density of data (Checking if the data is dense or sparse)
2. Dimensionality of data (High dimensional or low dimensional)
3. Size of the data (for lower computation time)

Since:

-> Radial Basis is good for sparse & high dimensional data
-> Cubic Spline is good for dense data
-> Polynomial Interpolation is better for small and low dimensional datasets
as it can fit accurate lines/curves for functions upto 3 degrees.

My doubts are:

1) Is there a sure shot way of checking the density of the interpolation column's data distribution? Some techniques I have identified are:

1: If the number of missing/empty values is significant (>=50%) the data is sparse.

2: If the range of majority of the data values is small & the standard deviation is small, then the data is considered dense, else, sparse.

3: Visualization using a scatter plot.

2) Is the following concept regarding high & low dimensionality right?

If the number of dimensions/variables is the same as or outnumbers the number of rows, then the data is high dimensional, else, low-dimensional.

3) Can I include a rule in my code that if my data is low dimensional & the number of rows is less than 100,000 then it's a small dataset, else, large?

What I have tried:

I gathered the above points after a lot of research. Do let me know if my above points right.

Note: I understand that some of the above points like size of the dataset & differentiating between sparse & dense data distribution are subjective, but I want to know if they are accurate to a decent extent.