While I was reading about filter design in this article: http://www.apogeeweb.net/article/35.html, you can also find specific explaination about Butterworth filter here if you need. And going through the schematics, the following 2 questions popped up in my mind and I could not find a satisfactory answer to them:

1) A first order low pass butterworth filter may be designed as shown below:

and a basic second order low pass butterworth filter as

But if we are to design a higher order filter, we don't just put another RC segment in the non-inverting terminal, instead, we cascade a combination of first and second order filters. Why is it so, I mean, why don't we just add another RC segment? Closed loop stability issues?

2) A band pass filter can be constructed by cascading a low pass filter to a high pass filter with the frequency cut-off constraints. Does it make any difference which segment is added first, like 1st Order High-Pass Butterworth and then 1st order Low-Pass Butterworth, would it be any different from 1st Order Low-Pass Butterworth and the 1st order High-Pass Butterworth Filter?

Regards

 

But if we are to design a higher order filter, we don't just put another RC segment in the non-inverting terminal, instead, we cascade a combination of first and second order filters. Why is it so, I mean, why don't we just add another RC segment? Closed loop stability issues?

No, loop stability is not the issue. The problem with simply inserting additional RC segments is that without the operational amplifier to provide a buffer between RC sections, the sections interact with one another to produce a response that deviates significantly from an ideal Butterworth response (i.e., flat response in the passband).

2) A band pass filter can be constructed by cascading a low pass filter to a high pass filter with the frequency cut-off constraints. Does it make any difference which segment is added first, like 1st Order High-Pass Butterworth and then 1st order Low-Pass Butterworth, would it be any different from 1st Order Low-Pass Butterworth and the 1st order High-Pass Butterworth Filter?

No.

 

But if we are to design a higher order filter, we don't just put another RC segment in the non-inverting terminal, instead, we cascade a combination of first and second order filters. Why is it so, I mean, why don't we just add another RC segment?

The op amp circuit uses a small amount of positive feedback to control the damping factor (Q) of the circuit and generate a sharper rolloff at the corner frequency then two simple cascaded RC filters can provide.

Below is the LTspice simulation of a 2-pole Sallen-Key Butterworth filter and two cascaded single-pole filters with buffers.
As you can see the Sallen-Key filter response (yellow) is flatter in the passband, and has a sharper rolloff after the corner frequency then the two cascaded RC filters (green).

 

This is not in response to your exact question, but I designed a fun little spreadsheet for cascaded 4th order multiple-feedback bandpass filter design and analysis.

If you are willing to download LibreOffice, you may gain some insight playing with it.

Here's the thread with the downloadable spreadsheet.