I am working on my own logo and would like to use the fonts installed within Adobe Illustrator application (open type ,TT,etc) for my logo, can I use these fonts commercially?
2. Questions: Do these files have to be in PDF format only? Or is it acceptable to convert text into outlines?
3. Questions: Are fonts installed in Adobe Illustrator also web fonts and if not, why not, hence RBG (Web) or DMYK (print) color modes are selectable ?
It is unclear by what you mean by fonts installed within (the) Adobe Illustrator application. There are Adobe fonts that may be installed on your system by the installation of Adobe applications. And then there are any other fonts that may have been installed as part of the operating system, Microsoft Office, other applications, or otherwise installed by you that are enumerated and usable from within Adobe Illustrator.
Fonts that are installed by Adobe are usable for commercial purposes as long as you don't distribute the font files themselves. You can embed the fonts in .PDF, .EPS, or .EPUB files, for example. There is no subsequent royalty on distribution of such files with the embedded fonts. And there is no restriction against using the fonts within logos or any commercial design. You should not mess up a logo by converting text to outlines (lowers quality). What you can't do is bundle the fonts in applications or in web page streams. (Adobe's Typekit service provides for web page font usage!)
However, fonts from other sources depend strictly on the end user license agreement (i.e., the license) associated with such fonts. They may or may not provide as liberal terms of usage as fonts from Adobe. It is your responsibility as a designer to find out the terms of such licenses. We cannot provide that information here, unfortunately.
For logos for print purposes that will be used by placement in Illustrator or InDesign documents, PDF is the preferred format. For legacy workflows, .EPS (with fonts embedded) may be satisfactory. If you need a logo to be placed in a Microsoft Office file, you will likely need to punt by converting text to outlines and saving as either a .WMF or .EMF file.
The term “web fonts” has any number of meanings although the bottom line is whether the font (a) is in a format that can be distributed for use on a web page and (b) whether the font's license allows for such usage. As indicated above, the typical Adobe fonts do not allow for such usage except via the Typekit service.
RGB versus CMYK are irrelevant with regards to fonts in general and web fonts in particular. RGB or CMYK are the color mode for particular objects including text and the font usage is not restricted to one or another. (Furthermore, RGB is not restricted to web use.)