(1) I want to insert into a Text cell conventional *in-line* mathematical notation like $\lim\_{x\to a} f(x)$. 

I know I can do it by typing the StandardForm `Limit[f[x], x -> a]` in an Input cell, convert to Traditional Form via a Cell menu item, then paste the result into the Text cell. Or, per comment by @Bob Hanlon, type it into the text cell, select it, and use Evaluation menu item "Evaluate in place".

Is there some quicker way to do that, by means of a keyboard sequence or palette?

[I looked at the Classroom Assistant palette, but there seems to be no button to enter a limit expression other than in StandardForm (which is a bit strange, given the buttons in that palette for entering traditional forms for sums, products, derivatives, and integrals).]

(2) What about the conventional *display* mathematical notation like $$\lim\_{x\to a} f(x)$$
where the $x \to a$ is *below* the $\lim$ part?

Is there some reasonably easy way to get that?