Yes, you can start a Sun square any Sunday except when the Sun is in fall or detriment (so Libra or Aquarius). It is still worth doing it.
As far as the decrease in power of a random sign relative to domicile and exaltation I personally wouldn't know how to answer you. It is difficult to put these things in a concrete perspective, they are not numbers or physical formulas. However, if you are trying to choose if it's better to begin a Sun square now or to wait for March when the Sun will be in Aries, I would say it depends on what do you need it for. If for example you are facing some hard transits and need protection, I'd say spam it, the more the better. If you need to do a Sun square for some specific aspect of your life, but nothing urgent, maybe you could wait till a more favorable placement, and do other kind of more priority stuff in the meanwhile