Yes, you can cast spells with a Material (M) component without issue.
Your Holy Symbol takes care of it.
This is one of the more difficult things to look up in the current 5e rules. It starts on page 58, under Cleric spellcasting:
You can use a holy symbol (found in chapter 5) as a spellcasting focus for your cleric spells.
In the equipment section, page 151:
... A cleric or paladin can use a holy symbol as a spellcasting focus, as described in chapter 10. To use the symbol in this way, the caster must hold it in hand, wear it visibly, or bear it on a shield.
Finally, page 203, under Material (M):
A character can use a component pouch or a spellcasting focus (found in chapter 5) in place of the components specified for a spell.
Put it all together: You can use a visibly worn holy symbol (no hands required) in place of the material components for a spell.
Somatic Components
What's more likely to trip clerics up are somatic components, which ALSO require a free hand but aren't covered by the holy symbol.
Fortunately, the rules are pretty lax on this point. Page 203 outlines interacting with objects:
You can also interact with one object or feature of the environment for free, during either your move or your action. For example, you could open a door during your move as you stride toward a foe, or you could draw your weapon as part of the same action you use to attack.
(See this answer for more info)
A very strict reading of this would allow the cleric to sheath his weapon, cast his spell, and then draw his weapon again the next turn (giving up opportunity attacks for a turn).
OR, you can drop your weapon (free), cast your spell, and then use your free interaction to pick it up again.
OR, pick up the War Caster feat (as you have).
OR, just ask your DM to go easy on you...
No, the player would attack with disadvantage.
As per the restrained condition:
Attack rolls against the creature have advantage, and the creature’s Attack rolls have disadvantage.
This does not mention any exceptions for spell attacks, even ones with only verbal components. All attack rolls the creature makes while restrained then have disadvantage.
However, the point is nearly moot because there are no existing spells that are verbal only and require an attack roll. The Sorcerer metamagic subtle spell could be used to create such a case, however, which should be ruled as above.
Best Answer
Yes.
Only spells with a Somatic component require that you have a free hand.
War Caster states:
It does seem a little odd that the War Caster rules would bother talking about having only one hand full. I believe the purpose of the War Caster feat is to allow you to perform somatic components when you have both hands full.