Yes, it’s possible to do a Birch reduction of toluene using sodium metal.

No, because only the OH bond is broken giving the alkoxide. The C-O bond is unaffected.

Well, that is an excellent question. The prevailing opinion is that the blue color of sodium dissolved in liquid ammonia is due to solvated electrons, and it is the electrons that perform the reduction. One could (and it is has been done) alternatively use electrochemical means to perform these reactions. See: http://openflask.blogspot.com/2019/02/e-birch.html
In those cases, it appears that reduction is not due to free electrons, but occurs at the surface of the electrode.

Glad to hear it. Thanks!

Best approach if you are looking to reduce off a bromo group is just to employ lithium halogen exchange with n-butyllithium or t-butyllithium depending on whether it’s sp2 or sp3. Very clean and fast reaction.

A very low temperature is required because the boiling point of ammonia is –33 °C. Ammonia is a gas at room temperature, which makes it unsuitable.
In order to obtain liquid ammonia, ammonia gas is passed through a flask attached to a coldfinger apparatus (usually dry ice / acetone).

The resulting (sp3) carbanion would be many orders ( >10) of magnitude less stable than the (sp2) carbanion, and sodium doesn’t have the reduction potential to make that possible. One exception is alkenes adjacent to an electron withdrawing group (such as an ester) which can stabilize the negative charge. It turns out the pKa of the resulting anion is a pretty good guide to what species can be reduced.

No, it’s trans-2-butene.