Learn Spanish (Latin America): Quiero ver algún estilo en mi talla.

Because it comes right before the masculine singular noun estilo. When alguno (some/any) is placed directly before a masculine singular noun, it drops the final -o and gains an accent, becoming algún.

The translation says "some styles" (plural), but the Spanish says algún estilo (singular). Why?

In Spanish, when you are talking about "some" or "any" of an item in a general sense, it is very common to use the singular form (algún estilo) rather than the plural (algunos estilos). English prefers the plural "styles" in this context, which is why the translation differs, but the singular is much more natural in Spanish here.

Can I use tamaño instead of talla for "size" here?

No, because talla specifically refers to clothing or shoe sizes. Tamaño refers to the physical dimensions or volume of an object (like a large box or a small dog). Since this sentence is about clothing styles, talla is the correct word.

Why is ver not conjugated?

Because it directly follows the conjugated verb Quiero (I want). When two verbs are paired to express a single idea (like "I want to see"), only the first verb is conjugated. The second verb stays in its infinitive (dictionary) form, which is ver.