I would like to see if there is clothing that can provide sun protection while minimizing sweating and/or allow air flow.
Would also like to do the same with my bike helmet without compromising safety.
Many items of quality cycling clothing from reputable brands with high SPF are available. Under-helmet caps with the sun protection are available as well.
Since this site doesn't do product recommendations you'll need to browse producer and retailer sites.
To quote the Wikipedia page for "Sun Protective Clothing":
A number of fabrics and textiles in common use today need no further UV-blocking enhancement based on their inherent fiber structure, density of weave, and dye components, especially darker colors and indigo dyes. Good examples of these fabrics contain full percentages or blends of heavy-weight natural fibers like cotton, linen and hemp or light-weight synthetics such as polyester, nylon, spandex and polypropylene.
What that means is that most common cycling gear like jerseys (typically polyester), shorts (nylon + spandex), arm- and leg-warmers (ditto) is already basically UV-blocking. The exception would obviously be for fabric made as an open weave or mesh for breathability. (I once got an interesting pointillist sunburn through the mesh panels of a non-cycling workout top.)
Anecdotally, I can say that in >20 years of cycling, including some long 12-hour days in the sun, I've never once gotten a burn through solid-fabric cycling gear. (The knitted backs of certain cycling gloves, on the other hand...)
So there is no need to replace existing cycling gear with new just to get "UPF 50+" fabrics. You're just looking to cover up skin that you would previously have exposed to the sun.
In my case that meant shopping for a cap to wear under my helmet and lightweight arm and leg protection. I also had a strong preference for a white colour, since if it's cool enough to wear black it's probably also cool enough to wear my arm-warmers. (Similarly leg-warmers or tights.)
Fortunately my LBS had several styles in stock to compare. The black UPF 50+ arm protection were virtually indistinguishable from "normal" arm-warmers except for a 20% price premium. There were 2 comparable (same price-point) white UPF 50+ arm products from different manufacturers; one was significantly thicker and heavier than the other. (It was almost merely a white version of an arm-warmer.) The lighter ones feel like they have a slightly tighter weave, but seem to have excellent breathability and have worked fine for me in practice.
I would definitely recommend trying to find a place to check any products out in person, rather than buying them sight-unseen online.
Note that you will still want to carry a small amount of sunscreen so you can apply it to places where you're not completely covered up; a problem spot for me seems to be the bones of my wrists where the cycling gloves don't quite match up to the arm protectors.