[RPG] Do you have to have a Holy Symbol in one of your hands to use it

You can use (almost) all of your powers when disarmed and without implements.

Implement^DDI and Weapon^DDI powers don't prevent you from using them if you lack the appropriate tool: they simply allow you to get a bonus when you have the appropriate tool.

When using an Implement (keyword) power you make an unmodified ability check (usually Wisdom-based for Implement Cleric powers) against the target defense (as per definition of attack roll).

When you hold a magical implement (e.g.: a holy symbol), you get to add the implement's enhancement bonus to both attack rolls and damage rolls with Implement powers (and a damage boost in case of critical hit).

Also note that you can take advantage from any implement you are proficient with (not only holy symbols). If your Cleric took the Arcane Initiate^DDI feat, then he can use even magical staves, wands and orbs to improve his Cleric powers.

A non-magical implement does not provide any bonus (except for flavor or feat support) unless it is a superior implement. Superior implements cost more but provides a varied array of advantages (properties similar to those of weapons).
For example, the Astral Symbol^DDI costs 18 gp but has the Distant (+2 range of ranged and area powers) and Energized (radiant) (+2/+3/+4 damage bonus with Radiant powers) properties. Its base version is non-magical, but it you can buy or create an enchanted version of it.
You gain proficiency with a single type of superior implement by taking the Superior Implement Training^DDI feat.

Lack of proficiency with an implement you are using means that you gain no advantage from its superior or magical bonus and properties.

When using a Weapon (keyword) power while unarmed, you make an unmodified ability check (usually Strength-based for Weapon Cleric powers) against the target defense (usually AC).
However, unarmed attacks have no proficiency bonus, so you lack a thick +2 or +3 modifier.

When you wield a non-improvised weapon you get a proficiency bonus to attack rolls with Weapon powers.

When you wield a magical weapon, you also get the weapon's enchantment bonus to attack rolls and damage rolls with Weapon powers (and a damage boost in case of critical hit).

Lack of proficiency with a weapon you are wielding means that you don't apply the weapon's proficiency bonus and gain no advantage from its magical bonus and properties.

Some powers may require you to wield specific weapons or implements. In this case, they explicitly state this requirement in their Requirement line of the power block. This is usually found in Rogue powers, for example.

No

A Ki Focus is a category of implement, like Staff, Holy Symbol and Rod. This would be like asking if a Wizard who multiclassed Cleric could use a Holy Symbol as a Staff. They're just different things.

If you look on PHB3.p62 you'll see that the monk has "Ki focuses, weapons with which you are have proficiency" listed as the implements that they can use. The "Monks and Weapons" section is just an elaboration on this, explaining that you can use weapons as an implement, or use a ki focus. It also elaborates to say that if you use the magical properties of a Ki Focus you still get to apply weapon specific feats if you are using an attack power with the weapon keyword.
You can also use a weapon as an implement, in this case all the appropriate weapon feats apply to implement attacks.
If you use an implement attack with a Ki Focus, there is no way to also benefit from a weapon feat, with a wording like "when you attack with a light blade" like Nimble Blade.

So ultimately, if you multiclass Cleric, you can now use Ki Focus, Holy Symbols and weapons with which you are have proficiency as implements. To compare these 3 options:

• Holy Symbol: can not be used on Weapon attacks, only a problem for melee basic attacks, as no monk attack has this keyword. No weapon feats apply no matter what you hold in your hand.
• Ki Focus: can be used on any attack that has the Implement or Weapon keyword. No weapon feats apply no matter what you hold in your hand.
• Weapon as Implement: can be used on any attack that has the Implement or Weapon keyword. Benefits from any appropriate weapon feat.

Weapons can benefit from Shards as well, so from an optimization standpoint they are wastly superior to other types of implements for most builds.