All the methods you have used are correct. Using the character ﷽ as such is correct too, provided that the HTML document is UTF-8 encoded and declared to be UTF-8 encoded. The ﷽ and ﷽ notations work independently of character encodings (that’s one of the main reasons for using them).
However, it fails if none of the fonts in the user’s system contains a glyph for the character. Browsers then typically display a small rectangle to indicate this.
The font information page for the character at Fileformat.info has incorrect or incomplete information. If you click on the Local Font List link there, you should see the real situation in your system. In my system, a fairly normal Windows 7 with a fairly large collection of free fonts added, none of the fonts listed on the file info page except GNU Unifont actually contains U+FDFD ARABIC LIGATURE BISMILLAH AR-RAHMAN AR-RAHEEM. Perhaps the font support page was created in a system with versions of Arial, Times New Roman, etc., that differ from the normal fonts shipped with e.g. Windows 7.
What’s worse, the GNU Unifont glyph is hardly suitable for any real use. Being a coarse bitmap, it is totally inadequate for rendering a calligraphic character with a large number of details.
Microsoft Uighur has an appropriate glyph, but this font is not free, and there does not be any easily accessible information on terms for getting it legally for use as an embedded font (web font). There is also a font called Universalia, with information available in Russian only and of questionable legal status.
The following image shows examples of the character (in very large font size) in the fonts mentioned.

If you can see the character in iPhone, then obviously the iPhone has a font containing it, but most probably you cannot use that font as embedded.
Unfortunately, this appears to mean that you cannot use the character on a web page so that works for all users, or even the majority of users.
Update: The good news is that Google Fonts: Early Access contains a few fonts that contain the character and can be used as embedded fonts, either as hosted by Google or as hosted on your server. Beware that Early Access fonts are more or less experimental and that the shape of the character might not be suitable for your overall design and style.
In the following examples, I have included a short phrase in normal Arabic letters for comparison.
<style> @import url(http://fonts.googleapis.com/earlyaccess/amiri.css); @import url(http://fonts.googleapis.com/earlyaccess/notonaskharabic.css); @import url(http://fonts.googleapis.com/earlyaccess/notonastaliqurdudraft.css); </style> <p><span style="font-family: Amiri">﷽ السلام عليكم</span> (Amiri) <p><span style="font-family: Noto Naskh Arabic">﷽ السلام عليكم</span> (Noto Naskh Arabic) <p><span style="font-family: Noto Nastaliq Urdu Draft">﷽ السلام عليكم</span> (Noto Nastaliq Urdu Draft)