[RPG] How many spell slots does a Level 3 Warlock have

All warlock spell slots are the same level (PHB p.107, under the Spell Slots section). As they gain warlock levels, warlocks eventually reach their maximum of 4 spell slots (at the 17th level of warlock), and their maximum spell slot level of 5 (at the 9th level of warlock).

Do note that you can cast spells with slots that are higher level than the base spell. For example: hold person, a second level spell, can be cast with any spell slot of level 2 or higher. If you were to cast it with a higher level slot, it would even count as a spell of that higher level. Many spells even specify additional effects when you cast them at higher level, though not all do, and they don't need to have such a feature in order to be able to use a higher level slot.

In addition, the reason for the relatively limited number of slots is that warlocks regain their spell slots on a short rest as well as a long rest (unlike most other spellcasting classes).

No, Warlock Spellslots do not count toward the Multiclass Spellcaster table

Spell Slots. You determine your available spell slots by adding together all your levels in the bard, cleric, druid, sorcerer, and wizard classes, half your levels (rounded down) in the paladin and ranger classes, and a third of your fighter or rogue levels (rounded down) if you have the Eldritch Knight or the Arcane Trickster feature. Use this total to determine your spell slots by consulting the Multiclass Spellcaster table. - PHB p. 164

Warlock isn't included in that list. Thus you would only have 2 1st level spells as a level 19 warlock, level 1 wizard PC. You could cast level 1 warlock spells using your wizard slots and cast known level 1 wizard spells using your pact magic. Granted you would be able to cast those level 1 spells at maximum level (as per usual with pact magic) but its not going to benefit you in comparison to Eldritch Master which allows you to double your spells per day effectively.