You built it.
Now own it.

Usually yes, and for a narrower reason than people expect: priority. A Swiss trademark gives you a filing date, and that date is what decides who wins if someone else adopts the same name later. Changing the name of a product that customers already know costs far more than filing does. If the budget genuinely is not there, do the clearance search first: it is the cheap half and it tells you whether the name is even worth building on.

It depends who wrote it. If your own employee wrote the software in the course of their duties and in fulfilment of their contractual obligations, Swiss copyright law gives the company the exclusive right to exercise the rights of use; the employee remains the author, and the rule covers software only, not the designs, texts or images around it. Freelancers and agencies keep the rights in what they wrote until they assign them to you, and an invoice marked paid is not an assignment. The fix is simple: a written assignment covering the code, the graphics and any material they brought in, plus confirmation that third-party components carry a licence permitting commercial use. This is the item investors check first in due diligence.

It depends. Extending becomes worth it when you start shipping into the EU, when a distributor asks, or when you see a similar name filed there. The Swiss + EU package exists for exactly that step, and the Madrid Protocol lets you add countries later from the Swiss registration rather than starting again.