What would be a safe dosage of each for someone 5'7 120 pounds? How long should this person wait to ingest the dmt tea after ingesting the rue tea? Is it a sitting down or laying down type of trip? Or is it a trip where you can walk?

imo a "safe" dose and if it's your first time is 4g rue and 3g to 4g acacia(brewed properly), you can ingest them at the same time i personally like to wait 5 mins after taking the rue, i've had success with waiting 20-30 mins, this is a profound but not a full immersion dose you can still walk if necessary
good luck

The A. confusa [its root bark, right?] will be the variable. Its potency is less consistent than P. harmala by quite a bit. Plan for the first few trips to just be spent finding your proper dose.
I'm roughly your size and weight and I bought a kilo of cheap confusa, knowing it might be somewhat weak, and dosing it with 3.5 grams rue 2 grams was just enough to know I took a psychedelic besides just rue, 4 grams gave me faint CEV's a feeling for the personality of the stuff and an appreciation of physical pleasure, 8 grams gave me a more traditional trip, and 12 became my favorite or at least most repeated trip.
I dont mean to say those doses will work that way with your material, yours could be twice as potent, but if you approach it in that way you'll be less likely to be radically overwhelmed and you'll learn some about it at each stage.
Its a very good idea to keep notes. When I'm tripping a white computer screen is almost blinding. theres a free app called 'NoteTab Light' thats like windows notepad but lets you change colors. Mine is a black background with dark orange text, I can look at that no matter how hard I'm tripping

Does the amount of time you wait affect the trip significantly? For example, would waiting 5 minutes make the trip stronger than waiting 20-30 mins?

Varies from person to person, and from day to day for same person. Inevitable variables make hard conclusions impossible. There are fans of different styles, for me it doesn't matter all that much. Don't overthink too much, you can't 'tune-up' your trip to become such or so by having a watch in your hand