How do I size a mini pump to the air conditioner's capacity?

As a rule of thumb allow roughly 0.5 l/h of condensate per 1 kW of cooling capacity in humid conditions, but what counts is the pump's flow at your actual lift, not its maximum rating. A typical 2.5–5 kW split is covered by an 8–14 l/h pump; read the duty point off the Q-H curve for your head and run length.

Peristaltic or impeller (float) pump?

A peristaltic pump mounted in the trunking is the quietest and stays hidden, but has lower flow and needs periodic tube replacement. An impeller pump with a float sensor in the tray gives more flow and higher lift, suiting cassettes and ducted units, but is louder and needs space.

Does a mini pump have an alarm contact to shut the unit down on failure?

Most pumps include a volt-free NC alarm contact that, on high water level, cuts power to the compressor or signals the unit to prevent overflow. Always wire this contact into the unit's control circuit on install — it is standard protection, not an option.