I've now read the first of your links:
https://assets.gov.ie/6740/96a264d9ee6f427b8d53c6d9d966f0fb.pdf

I did ask for a link to significant scientific evidence that global temperature increase is caused purely by cyclical variations of the earth and sun.

The above link doesn't provide me with that.

It puts forward a hypothesis that periods of high solar activity (as recorded in records of numbers of sunspots) coincide with higher temperatures - at least, I think that's what he's saying, he's not very clear - and that this could be responsible for global warming.

The most obvious point to say about that is that even if this hypothesis were correct, it does not preclude CO2 emissions (man-made or otherwise) having an effect. Does he or does he not think CO2 emissions increase global temperature? He presumably thinks so but doesn't say much on it. (More on this later)

He does say "The twin effects of NRSA & RHO must be taken jointly into account as climate influencers. As yet there is no consensus on how the size of these effects compares with that of CO2 as a greenhouse gas." That's a very ambiguous statement but it certainly admits that not many people think these effects are comparable with CO2!

The idea that, whether or not his hypothesis on solar variation is true or not, it says nothing about the existence or potency of man-made carbon, it turns out did not just occur to me: it has, google reveals, also occurred to plenty of those criticising the theories of Willie Sooner, who your man Tony quotes.

He makes a lot of fuss about a more severe winter in 2017-2018 (in specific parts of the world, Ireland being - I'd have to check whether these were more severe across the globe) but says absolutely nothing about the summer of 2017. Or any other summers. Talk of wether other parts of the year back up his cooling idea are conspicuously absent. The summer of 2018 certainly has not inspired confidence in the idea of a cooling sun.

He has a page where he talks about how climate models should discount El Nino event years. Many climate scientists do this in their modelling, and can still point to global surface temperature rises as worrying. Plenty of climate scientists have been factoring El Nino before this guy pointed that out.
e.g.
https://www.carbonbrief.org/interactive-much-el-nino-affect-global-temperature


What I can't understand is his assertion that "This over-estimation [i.e. due to El Nino events] means that some other factor or factors were co-contributors to 20th century warming". Eh? No, surely it just means that it's hard to draw firm conclusions about what is happening to global temperatures in specific El Nino event years!

Reading around the topic, there seems to be many more scientists sceptical about solar influence of this kind:
https://www.ucsusa.org/resources/how-does-sun-affect-our-climate