I can reproduce this, and not just in XeTeX but in other applications. (Spoiler: There's no bug.)

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Minimal example

First, I reduced your files to a real minimal example:

\documentclass{article} \usepackage{fontspec} \newcommand{\txtital}{{\itshape f g}} \newcommand{\numb}{1} \newcommand{\CharVar}[2]{{\addfontfeature{CharacterVariant=#1}}#2 {\tiny(CharacterVariant = #1)}} \newcommand{\StylSet}[2]{{\addfontfeature{StylisticSet=#1}#2 {\tiny(Stylistic Set = #1)}}} \begin{document} \setmainfont{Andika New Basic} \numb \CharVar{1:0}{\numb} \CharVar{1:1}{\numb} \setmainfont{Calibri} \txtital \StylSet{4}{\txtital} \StylSet{5}{\txtital} \end{document} 

which produced:

where it appears that your problem is fully reproduced. You will shortly see why starting with actually minimal examples is useful.

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Issue 1 of 2 (Andika New Basic)

Firstly ignore the hyphen after cv01- that you got; it's just a bug in the macro in the answer from which you copied it; I've left a comment there.

Anyway, let's look at why it doesn't seem to take effect...

A closer look reveals that your \CharVar{1:0}{\numb} expands to:

{{\addfontfeature{CharacterVariant=1:0}}\numb {\tiny(CharacterVariant = 1:0)}} 

where your test text \numb is outside the {\addfontfeature{CharacterVariant=1:0}} group. So the \addfontfeature has no effect on the text. You can fix this bug in the macro by writing the text as

{\addfontfeature{CharacterVariant=1:0}\numb {\tiny(CharacterVariant = 1:0)}} 

(always best to start with the dumbest and most explicit code), testing that it works, and then fixing your macro to, say:

\newcommand{\CharVar}[2]{{\addfontfeature{CharacterVariant=#1}#2 {\tiny(CharacterVariant = #1)}}} 

which works: produces

So there is no bug here: the font feature (cv01 or "Digit One without base") is documented, detected, selectable, and effectual.

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Issue 2 of 2 (Calibri)

With Calibri, things get more interesting. As you saw, XeTeX did not detect a ss05 font feature. But it's not just XeTeX: here's otfinfo:

% otfinfo -f /Library/Fonts/Microsoft/Calibri.ttf c2sc Small Capitals From Capitals calt Contextual Alternates case Case-Sensitive Forms ccmp Glyph Composition/Decomposition cpsp Capital Spacing dlig Discretionary Ligatures dnom Denominators frac Fractions kern Kerning liga Standard Ligatures lnum Lining Figures mark Mark Positioning mkmk Mark to Mark Positioning numr Numerators onum Oldstyle Figures ordn Ordinals pnum Proportional Figures salt Stylistic Alternates sinf Scientific Inferiors smcp Small Capitals ss01 Stylistic Set 1 ss02 Stylistic Set 2 ss03 Stylistic Set 3 ss04 Stylistic Set 4 subs Subscript sups Superscript tnum Tabular Figures 

which is the same set of features detected by XeTeX.

In even more detail, one can install fonttools and run ttx on the font to get it in human-readable XML format:

% ttx -o Calibri.ttx /Library/Fonts/Microsoft/Calibri.ttf Dumping "/Library/Fonts/Microsoft/Calibri.ttf" to "Calibri.ttx"... 

and it dumps all the tables. If you open the file Calibri.ttx in a text editor, you'll find that it contains mentions of ss01 through ss04, but no ss05.

And yet another source: if you load Calibri.ttf into opentype.js, the results are similar.

But the regular system application TextEdit (on macOS) seems to do something interesting: if you type fgfg into it, select Calibri as the font, italicize the last two characters, select them, and then go to Show Fonts → [Gear symbol] → Typography → Alternative Stylistic Sets, there is a Stylistic Set 5, selecting which does change the shape of the f (as XeTeX did):

What magic is this? How are TextEdit (and XeTeX) able to select a stylistic set which is clearly not present in the font, as confirmed from so many distinct sources?

Well, a little bit of thought will lead you to the answer :-)

% otfinfo -f /Library/Fonts/Microsoft/Calibri\ Italic.ttf c2sc Small Capitals From Capitals calt Contextual Alternates case Case-Sensitive Forms ccmp Glyph Composition/Decomposition cpsp Capital Spacing dlig Discretionary Ligatures dnom Denominators frac Fractions kern Kerning liga Standard Ligatures lnum Lining Figures mark Mark Positioning mkmk Mark to Mark Positioning numr Numerators onum Oldstyle Figures ordn Ordinals pnum Proportional Figures salt Stylistic Alternates sinf Scientific Inferiors smcp Small Capitals ss01 Stylistic Set 1 ss02 Stylistic Set 2 ss03 Stylistic Set 3 ss04 Stylistic Set 4 ss05 Stylistic Set 5 subs Subscript sups Superscript tnum Tabular Figures 

and similar results with ttx or opentype.js or indeed even XeTeX:

\documentclass{article} \usepackage{fontspec,etoolbox,expl3} \setmainfont{Calibri Italic} \def\somefontfeatures{ss01, ss02, ss03, ss04, ss05, ss06, ss07, ss08, ss09, ss10} \ExplSyntaxOn \newcommand\listsomefontfeatures{% \renewcommand*{\do}[1]{ \fontspec_if_feature:nTF {##1}{##1,\ }{} } \expandafter\docsvlist\expandafter{\somefontfeatures} } \ExplSyntaxOff \begin{document} \listsomefontfeatures \end{document} 

That's all there is to the mystery: the stylistic variant ss05 is present in the Calibri Italic font, but not in the Calibri font. This is consistent with everything you saw in the question, and, again, there's no bug in XeTeX's detection or selection of font features.