Hi there! I'm sorry it took me so long to respond (this is a topic near and dear to my heart, lol), but it's been a very hectic week at work.
No, you are not the only one to deal with this issue. The saying is that "men sweat, ladies perspire." No. Hell no. I freakin' sweat like a damn pig. It sucks, I know. When I had short hair, there were multiple times when I'd have sweat literally dripping off the ends of my hair 15 minutes into a lesson. While I'm not exactly thin now (5'4", 150), I was much thinner when I started dancing...it didn't make a difference, so I doubt it has to do with size or athleticism. It isn't just lesson- or dance-related; any time I have to interact with people (which is, you know...always), I get nervous and sweat. I plan what I wear around what meetings I have during the day; even though I've known most of my coworkers for 14 years, I still get nervous and sweat through my clothing when I have even a social conversation with them. I've had notes, stuck in my back pocket, end up illegible because I sweat so much that I sweat through my jeans and the ink ran. It sucks. Hard. I really, really get it.
You're not the only one. Take a shower and wear clean clothes and deoderant, so your sweat isn't stinky. Bring a towel to mop yourself off. Wear clothes that don't show sweat. Wear clothes that you are comfortable in, that will help keep you cool. Pants+cami+shrug is good, because it will leave your lower back, chest, and neck bare or with only a thin layer, but will keep sweat off direct contact with a leader's skin. Other than that...there isn't much you can do.
If you sweat more when you're nervous (like me), then trust that that will end eventually.
Think of it this way: you WILL burn out. Accept it, accept it as part of the learning/growing process, and move on. Enjoy what you've got now. If four lessons a week is working for you, let it work and enjoy it. When it stops being enjoyable (or when you start getting conflicting information that's holding you back instead of helping you forward), then stop. But don't stop what you enjoy now because of the fear of some possibility in the future.
I don't know about online vendors, but I'd suggest putting more thought into technique. You shouldn't be getting stepped on that regularly. Most of the damage that was ever done to my feet I managed to do to myself (because I am just _that_ talented!).
As an introvert, who is painfully shy, who has spent a lifetime cultivating the art of being a wallflower, who can disappear from a room or a one-on-one conversation quite effectively...I say go. Don't let your fears make it out to be more scary than it is. There is _always_ a quiet, dark corner to hide in. But even so...the more you build it up in your mind, the scarier it will become. It can become paralyzing; don't let that happen. Go, and adjust your expectations. Go, and think about just going and seeing what it's like. If I can go to milongas, by myself (and even after six (?) years, I still get almost sick to my stomach before walking in), then so can you. Who cares about three months? What's so magical about three months anyhow? Go. Enjoy yourself. Warn leaders that you are a beginner when (WHEN!) they ask you, but don't apologize for that. Everyone starts somewhere. Just go. Don't build it up in your mind to be more than it is.
"None of us is bleeding. None of us fell on the floor. I'm having a good time. It must have been good enough!" Seriously. I've bled, I've fallen, I've not had a good time. And so what? It's just dancing. Say you're a beginner so you don't know well enough to tell. They should know better than to ask at a milonga anyhow! ;-)
No clue.
I smoke. When I'm standing outside smoking, particularly when I'm in heels, I practice crossing one foot over the other smoothly. Forwards and backwards. My teacher noticed. I do molinetes around my cats' food dish when I'm waiting for something in the kitchen. I don't exercise...pretty sure I'm allergic. (Which is why I weigh as much as I do. So sue me!

)
More seriously...any cardio is good. Pilates is good for being aware of your posture and your core. Wearing heels lots and learning your balance in them, and strengthening your ankles is good. Releves are good.
I always wore jeans, or jean shorts for lessons. Some people find that offensive...that's nice. My lessons, don't care. For milongas...not so much. I'm not much of a skirt kinda girl. Why be intimidated about asking? "So...this is kind of a strange question, but...I really like your skirt. Where did you buy it?" Done and done. No biggie. (Again, I say this as someone who is intimidated by pretty much everyone. Seriously. When it comes to social anxiety evaluations, I score in the highly socially anxious range. Socially inept. If I can do it, so can you.)
I don't know those songs offhand. I suck at names--of people, of songs, you name it. I'm personally a fan of compilations. Failing that, take the songs you like...find out who wrote them and/or who performed them...then take those answers and find more recordings of songs written/performed by the same group.
You're welcome! Welcome to D-F! It's nice to have a new face, of someone new and enthusiastic! (It brings back so many wonderful memories.)