If an agent I admire gives me personal feedback on a full can I send them a handmade card thanking them for my rejection? Or does that make me a weirdy?
Not weird--we get these occasionally. But email is a bit more the norm. Stick to 3-5 lines about how much you appreciated their time. Don't tell them you'll resubmit ASAP or that you disagree with them. Also (I know you wouldn't, but some authors do) sound sad, defeated, or angry. Wait until you feel better.
If an agent asks for a full, and I submit--but then decide to take my first three chapters and throw them in the garbage, can I resubmit?
Errr. Well...it's better if you don't. Sometimes authors resubmit four or five times, and then I get mildly miffed--especially if I read one version already and now I have to read the thing again. You might, instead, send a cordial note saying, "Hi. I've had a friend/outside editor [if it's true] look at my work, and we agree that the first three chapters can go. Just in case you haven't read this yet, it might be wise to start at the beginning of chapter four, which is page ___. I'm sorry for the inconvenience--I know you're busy."
If I made a fool out of myself and queried my novel with the lamest-est (that's right... so lame it deserved an extra -est) query ever then when I get my act together, should I send it to Agent McDream again?
Wait on that. This is why we suggest being absolutely, totally, 100 percent sure you're ready before sending your query. Often, authors feel a strange urgency--as if they must get their work to the agent that very moment or else...it's too late! (I'm not sure where this feeling comes from, but many authors get it.) Many people will say that the official answer is, "Too late, too bad, you get one shot."
Unofficially (she says in a stage whisper) you don't only get one chance. Wait for this round of rejections (if that's what happens--you may be surprised!) and if everyone says no, then wait six months, re-title your work, get yourself a new e-mail address, change your name around (use the initials of your first and middle name + your last name, say), make up a perfect query, and send it again. But other agents may tell you this is evil advice. You certainly won't get in trouble--the agent likely won't notice--but my colleagues would not be thrilled at my advising you to make more work for them.
When an agent addresses me by my first name in an email, do I start my response email with "Dear First Name" or am I supposed to remain on last name terms... and if I DO remain on last name terms, do I look like a kid trying to wear her daddy's suit?
I can't give you a definite answer there. I think it's kind of amusing when people call me by my last name preceded by a Ms., but I'm on a first-name basis with all of my authors. The best way to know is to look and see how they sign their correspondence. If it's their first and last name, stick with Mr./Ms. If it's their first name only, and they've been uber-casual, you can go ahead and use that. But you won't look like a kid in Daddy's suit--you'll look like a professional.
How far back to you send letters to agents that have your partials and fulls letting them know you HAVE representation? How do you get through that end sticky part where you are getting offers, etc. and have to pick an agent so that you don't burn bridges?
Well--that's a good question. Another reason, also, to try to send all of your queries out in one big round--that way, you get all of your answers, and do all of this notifying, at once. I'd say anyone who got your partial or full in the last 4-5 months and hasn't replied should get a quick note. If they don't know who you are, or don't want your work, they won't respond. No harm done.