You want to add the following code to your cell (at the cell level):
FractionBoxOptions->{AllowScriptLevelChange->False}]
Basically, you want to prevent script level changes inside from the fractions, without allowing any surrounding boxes (like GridBox) to interfere with their own opinions.
You can also do this at a higher or lower level interactivly by selecting something, opening the options inspector, searching for FractionBoxOptions, and toggling AllowScriptLevelChange.
As for your second problem, I think you'd want a cell containing two inline cells, each own with its own alignment.
CellPrint @ Cell[
BoxData[FrameBox[RowBox[{
Cell["Hello\nI'm left aligned", "Text"],
Cell["And I am\ncenter-aligned", "Text", TextAlignment -> Center]
}]]],
"Text" (* or "Input", or whatever you want the overall style to be. *)
]
