Switzerland was close to being the most heavily defended nation in the world at the time, and invading it would have been a humiliating bloodbath with no upsides.
The Swiss, in addition to their mountains, fortresses, and nationanlism, had one other thing: their entire army was a mass of snipers. Basically, every single soldier was a a light-armed sniper. German could have invaded and taken the lowlands with some difficulty. After that, they would have been in a world of hurt, losing thousands of soldiers for no gain. Basically, it would have been pointless, risky, and far more harmful than helpful - kind of like the Soviets in Afganistan.
Not even remotely close to true. If you’d read the cites provided, the Swiss were only going to conduct a covering action in the lowlands, abandoning them as indefensible and leaving them (and 80% of the Swiss population) to the Axis. As to being ‘the most heavily defended nation in the world’: horsepucky. They were short on aircraft, tanks, anti-tank guns and artillery of any sort, much less of the modern variety. The entire defense plan was to fall back into the Alps where they would eventually be forced to surrender from hunger if they hadn’t already done so by enemy action. As to the every soldier in the army being a light-armed sniper - what exactly is a ‘light’ armed sniper? Snipers in every nation in the world used a 7.62-7.92mm or thereabouts bolt action rifle; Switzerland was no different. Describing every single one of their soldiers as a sniper by virtue of having a bolt action rifle is absurd; by that definition every soldier in every army in the world at the time was a sniper.
The fact is if the Axis wanted to, they could have taken Switzerland with relative ease. They had no meaningful reason to do so however, and as I noted there would have been a steep economic price to pay in the form of the loss of the rail tunnels that carried most traffic between Germany and Italy for the duration of the war.
While it is certainly the case that Hitler did not try to invade England during the war, and it may even be the casethat he couldn’t have successfully attempted it during the hostilities then engaged, it was definitely a possibility that England held in dire fear. What would Germany have done if it had gained control of the bulk of Europe and succeeded in taking the western Soviet states? Stabilize the eastern territory, consolidate in Europe, then turn to the British Isles.
How about a beachhead across the Channel from which to support an invasion of England?
The UK would have had to have been dealt with before a German invasion of Ireland could have been successful. by which time it would probably not even have been necessary anyway. A German invasion of Britain was never going to be launched via Ireland.