Learn French: Quelqu'un a une allergie ici. - Someone has an allergy here.

No, quelqu'un (someone) is a fixed word. It is always treated as masculine and singular, even if you know the someone is a woman. You always use it with the verb form for he/she/it, which is why we use a (has) here.

Do I pronounce the 'n' at the end of quelqu'un before a?

Yes! Because quelqu'un ends in a nasal sound and the next word (a) starts with a vowel, you link them together. This is called a liaison. When spoken out loud, it sounds like the 'n' attaches to the verb: kel-kuh-NA.

Since allergie starts with a vowel, why don't we drop the 'e' in une?

You might be thinking of la (the), which drops its 'a' and becomes l' before a vowel (like l'allergie). But the words for a/an (un and une) never drop their letters. Since allergie is a feminine word, it simply stays une allergie.

We are learning about ne... jamais (never). How would I use it here to say 'Someone never has an allergy here'?

To say never, you put ne and jamais around the verb, which is a (has). Because a starts with a vowel, ne shortens to n'. So the sentence becomes: Quelqu'un n'a jamais d'allergie ici. Notice that the word une changes to d' because indefinite articles (un, une, des) change to de or d' in negative sentences!