I've heard that big Shoulder supported cameras are "items of special interest" on the London Underground as they might be disguised weapons / explosives.
I occasionally have to travel with a built camera on the Underground and this is a concern but not a major one. UK armed police are fairly good at reading situations and having talked with a few are well aware of what an actual camera looks like.
What's more of a concern is getting a fine for filming without a permit and not being able to get home because TFL has banned me or something. Needless to say, I advise productions not to travel Cinema cameras on the Underground without a TFL escort. It's just asking for trouble.
I've seen gaffers hold up a heavy viewing glass up to check cloud coverage. They've all had a small square of thick black tape in the middle of the glass to cover the sun itself. Still seems risky to me.
Can't recommend looking directly at the sun ever, even through heavy filtration. UV radiation is not good for your eyes and the sun puts out a LOT of UV.
If you plan on looking at the sun regularly, get an official sun filter or glasses. Anything for viewing an eclipse should work but it might be tricky to see thin cloud coverage. And even then, I would avoid looking directly at the sun and looking for as short a time as possible.
As for best brand of gaffers glass, no idea. I'll let those that have more than none make recommendations