Text size changes when converting to outline

By default, Illustrator is set up to create text objects for printed page layouts. The physical size of letters in that paradigm are deceptive. There is a bunch of empty space around the letter that is included in that character size. The system works alright when laying out columns of text in a design grid. In some other kinds of graphic design work the same system doesn't work so well.

The Font Height Options feature is a recent addition to Illustrator. You'll have four choices. The default text sizing method is the Em Box. The other options are capital letter height, lowercase character height and ICF box. This feature helps a great deal in things like sign design. The Align palette has options to align point text and area text objects by their glyph bounds. That's another somewhat recent addition.

We do not (yet) have the option to align or distribute text objects with other objects via their baselines. Using Smart Guides is a work-around to manually move and snap text objects in the desired position.

Sure. In the menu of the Character panel there is an option to turn on the size options. And then you can specify the Cap height.