Sin garantía, el arreglo del televisor sale caro.

Sin garantía is a fronted prepositional phrase that sets the condition/context for the whole statement: in the case where there’s no warranty.
The comma signals a pause and helps the reader hear it as an introductory phrase. In everyday writing you might also see it without the comma, especially if the phrase is short: Sin garantía el arreglo del televisor sale caro.

In Spanish, sin + noun often omits an article and is understood generically: sin garantía = without warranty coverage (in general / in this situation).
If you want to be more specific (e.g., without the warranty that came with it), you can say sin la garantía.

Yes—context makes it clear. Arreglo can mean arrangement (e.g., un arreglo floral = a flower arrangement), but with something broken like a TV, el arreglo is understood as the repair.
If you want a less ambiguous word, la reparación is also common: la reparación del televisor.

In much of Latin America, televisor is very common for the physical device (the TV set). Televisión can mean the medium/service (television), and sometimes also the device depending on region.
Both exist; televisor keeps it clearly about the appliance being repaired.

Salir has an idiomatic use meaning to come out to / to end up costing. So sale caro is like “it comes out expensive” / “it ends up being expensive.”
Grammatically, sale is 3rd-person singular because the subject is singular: el arreglo.

Es caro describes something as inherently expensive (a general quality).
Sale caro focuses on the result/total cost once you do it—often implying you might not expect it, but that’s how it turns out. For repairs, sale caro is very natural.

The subject is el arreglo del televisor.
Sin garantía is just an introductory phrase giving the condition; it isn’t the subject.

Caro agrees with what is “expensive” here: el arreglo (masculine singular).
If the subject were feminine, it would change: La reparación sale cara.