You've raised an interesting topic here m&m!
Although I don't currently have the luxury to walk to work, and I can't make the 20 mile round trip very easily at the moment on my bike, I can answer based on experience from when I have had the opportunity to do so.
when walking/ biking to work, what do you wear?
If I'm walking then I just wear my normal work attire. When biking I'll go full lycra (or equivalent).
how do you not get sweaty?
This entirely depends on the weather. For walking, generally I won't build up much of a sweat as in the UK it's quite temperate. However, I did do a bit of walk commuting when working in San Francisco a few weeks ago. With the hills and the warmer weather I did get a bit sweaty but it was nothing that was massively noticeable to others.
Cycling? Yes I would get a bit sweaty. But a small towel to wipe any away and a change of clothes is enough for me to not smell throughout the day.
isn't your backpack heavy carrying. your lunch and change of clothes?
Yes. I used to have a rucksack that contained change of clothes, lunch, laptop etc. I have since moved to pannier bags that are mounted on the rack at the back of my bike. It's a definite reduction in the amount of effort needed to cycle.
Alternatively, try and reduce the load you're carrying by leaving items at work.
if you get sweaty and have no access to a shower, how do you prep yourself once you arrive at work?
A small towel to wipe away the excess sweat, a few minutes to air dry out, some anti perspirant for the armpits and a change of clothes. If the bike ride is enough to make you seriously sweat, and you have no shower available, then perhaps it's best to cycle slower or walk.
how do you protect yourself from all the UV damage? I'm planning on sunglasses, gloves, lots of SPF, umbrella but it would be very hot.
I generally wear sunglasses if the sun is out and I have to squint; after reading once that it protects your eyes for longer. If the UV is a genuine issue then I'd put on some sunscreen. Generally in the UK, during commuting times (i.e. not 10am-3pm when the sun is at it's strongest), there is little need for sunscreen and is beneficial for vitamin D production.
How do you protect yourself from smog, car pollution? I'm taking of wearing a mask but maybe that is overkill.
I don't wear a mask, but you might feel it necessary especially if you're in a densely populated area such as London or LA. It's about weighing up the benefits of reducing pollutant inhalation with looking silly!
How do you protect yourself from psychos or weirdos? I'm a small person.
The real question is how do others protect themselves from me? ;) In all honesty I can't answer from your perspective as I'm a 6'2" guy and over 200lb, but I generally just ignore others and they ignore me.