[RPG] Can an arcane focus boost spell attack or damage rolls

Bad News

• Arcane Focus and Holy Symbol appear to be different "types" of items.
• Arcane Focus lists: crystal, orb, rod, staff or wand
• Holy Symbol lists: amulet, emblem, reliquary
• So barring some special item (a crystal amulet?) you would need one of each.

Good News

You have flexibility here. From PHB 203:

A character use a component pouch or a spellcasting focus in place of the components specified for the spell... A spellcaster must have a free hand to to access these items, but it can be the same hand that he or she uses to perform somatic components.

So for most spells you can use any one of the following:

• A spellcasting focus.
• A component pouch. (25gp)
• The actual component listed in the spell.

You want to avoid juggling items and revealing your capacities. This means you have at least the following options:

1. Two necklaces (Crystal and Amulet). Grab the one you need for the spell you are casting. Could also be tied to your belt, but that's more obvious. Or you could tie them together on the same chain, they weigh 2 pounds combined and you get a free object interaction each turn, so "switching" is not a big deal.
2. One focus, one component pouch. If you wear your holy symbol, nobody knows about your arcane magic. The component pouch can easily be written off as cheap medicinal herbs or some special components. Use these only for your Warlock spells. You could even just use the same component pouch for both classes.
3. Pay close attention to your spells. Many of them don't require any Material components. For the Warlock: Eldritch Blast, Hellish Rebuke, Mirror Image, Misty Step, Ray of Enfeeblement are all usable spells with no Material Component. For the Paladin: Cure Wounds, Compelled Duel, Smites all require no Material components. You may be able to assemble a spell list with no Material Components required.

No, you do not add your spell-casting ability modifier to a spell's damage roll unless it is specified in the spell description. From chapter 9, page 196:

Damage Rolls: [...] When attacking with a weapon, you add your ability modifier - the same modifier you used for the attack roll - to the damage. A spell tells you which dice to roll for damage and whether to add any modifiers.

Modifying this rule would also undermine class specific abilities, such as the Warlock's Agonising Blast Invocation.

With regards to understanding the specific terminology you have highlighted -

• The spell attack roll, as outlined in the rules quotation you gave, only acts to "determine whether the spell effect hits the intended target" with any subsequent damage dictated by the spell description.
• The attack roll is 1d20 + the attack bonus.
• The attack bonus is equal to your spellcasting ability modifier + your proficiency bonus.