How do I talk to the machinists without ticking them off?

Yes on both of your questions. Walk the print with them, and never promise a date your boss before you've talked to the shop. I learned this the hard way my first year when I basically fast-tracked my own parts by going around the queue, and word travels fast on a shop floor. Took months to dig out of that hole.

Here's what worked for me. When you've got a new part, take the print over there and say something like 'I need this in about three weeks, does that work with what you've got going on?' Not 'when can I have it' but 'does this work for you.' Then shut up and listen. If they say it's a week and a half of work behind the current jobs, that's your real date. Tell your boss that number, and if the boss pushes back, that's a conversation for the boss to have with the shop lead, not something you absorb yourself. Also, bring them the drawing before it's final if you can. Something like 'this bracket is going to be machined, anything about it that's going to be a pain?' Old guys will tell you in five minutes that your corner radius needs a specific tool or your depth is going to chatter, and that feedback is free design education you can't get anywhere else. And when they catch something, actually make the change. Do that two or three times and you stop being just another kid with a drawing.

That thirty year guy you mentioned? Ask him a specific question, not a vague one. Not 'any advice for me' but 'on this part, would you fixture it on the mill or would you do it in the vise.' Specific questions respect his time and let him show what he knows. Then follow whatever he tells you, because if you ignore his advice after asking for it, you're done. One more thing, find out who actually runs the queue. There's usually a lead or a scheduler, and getting your job into the official queue beats chasing parts around the floor every couple of days.

One thing I'd add is to put a date and revision letter on every sheet you hand over, because the fastest way to burn goodwill in a shop is having a guy spend a morning on a bracket only to find out you'd tweaked a dimension after lunch and never swapped the printed sheet. I did exactly that once and the silence I got afterwards taught me more than any lecture coud. Also bring two copies, one for the lead and one that travels with the job, since prints have a way of vanishing into a pile of shop paperwork exactly when someone wants to check a radius.

Another thing that worked for me when I was the new kid: spend your lunch break in the shop instead of at your desk. I used to just lean on a bench and watch the old-timer set up a job, and after a couple weeks he started explaining what he was doing without me even asking. Next thing I knew my parts were getting squeezed in ahead of stuff from people who never left the office. Also learn thier names and what each guy actually runs. Asking Dave for a lathe job when Dave is a mill guy makes you look like you still haven't paid attention.