1) When you take the Attack action to make a melee attack, you can't replace subsequent attack with casting of a spell unless you have a feature specifically leeting you do so, such as Eldritch Knight's War Magic or Valor Bard's Extra Attack.
2) The summoning will specify. In the case of Spiritual Weapon it uses your Bonus Action.
Part 1
Now can a character with 2 attacks use once melee attack and then use a 1A spell follow up with a BA spell?
character with 2 attacks uses one or two melee attack(s) followed up with a BA spell?
Part 2
for spiritual weapon or some other summoned thing that is controlled by the caster.
When it attacks/moves does it take up any action or BA of the caster?
1) When you take the Attack action to make a melee attack, you can't replace subsequent attack with casting of a spell unless you have a feature specifically leeting you do so, such as Eldritch Knight's War Magic or Valor Bard's Extra Attack.
2) The summoning will specify. In the case of Spiritual Weapon it uses your Bonus Action.
So Barbarian/cleric... i should be able to use my 2 melee attacks and use shield of faith in one turn.. should i not?
Yes on a turn your Barbarian/Cleric can;
As long as you aren't Raging, anyway.
Indeed, While active, Rage follows the rules below