A spiritual weapon (created by the spell of the same name) uses your bonus action for movement and attacking. It does not have its own actions, bonus actions or reactions.
The Spiritual Weapon spell has a casting time of 1 bonus action and range of 60 feet. Breaking down the spell description:
You create a floating, spectral weapon within range ...
So, you use your cleric's bonus action to cast the spell, creating the spiritual weapon within 60 feet of your cleric.
When you cast the spell, you can make a melee spell attack against a creature within 5 feet of the weapon.
If a creature is within 5 feet of where you created the spiritual weapon, as part of the same bonus action you used to cast the spell, you can attack that creature with the spiritual weapon.
As a bonus action on your turn, you can move the weapon up to 20 feet and repeat the attack against a creature within 5 feet of it.
In every round after you cast the spell, for its duration, you can use your bonus action to move the spiritual weapon up to 20 feet and attack a creature within 5 feet of the spiritual weapon.
Since any use of the spiritual weapon spends your bonus action, your cleric still has a regular action (and reaction) available.
No.
The antimagic field suppresses all of the effects of the haste spell, but it doesn't end the spell. While a creature under the effects of haste is inside an antimagic field, none of the effects (positive or negative) of the spell apply, but the spell itself still exists and hasn't ended.
Similarly, if a haste spell does end while the affected creature is inside an antimagic field, then there will be no "wave of lethargy"; that is also an effect of the spell, and it is also suppressed.
Contrast the wording of antimagic shell (the spell whose effects define those of an antimagic field) with that of dispel magic (PHB p., 234, emphasis mine):
Choose one creature, object, or magical effect within range. Any spell of 3rd level or lower on the target ends.
Dispel magic explicitly ends spells; if antimagic field and similar effects also did so, they would explicitly say so.
Best Answer
No.
The description of the Antimagic field states (emphasis mine):
The emphasized part suggests that magic of any kind cannot exist inside this area: any connection between the weapon and the caster is interrupted. The Spells entry of the Antimagic Fields states (emphases mine):
The question is: is Spiritual Weapon active on the caster? The spell's description says (emphases mine):
There is a clear connection between the caster and the weapon; for the duration the caster can command the weapon via the magical link made by the spell: this means that the spell is active on the caster.
Therefore, the caster cannot use their bonus action to make the weapon move or attack while they are inside the AoE of the Antimagic Field: as soon as they exit from the dead magic area, however, they can resume command of the Spiritual Weapon (if its duration has not yet expired).