Are there any guidelines to introducing the second character in a two-hander? Can you bring him in at the start of the second Act or do we need to see him in the first Act (ex. Lethal Weapon)?
And in this instance the script would not be a confined space like your post about "P2". It would be a mentor/student cum surrogate father/son relationship.
This is one of those "it depends" questions. If it's a true two-hander, then it's going to be hard to avoid bringing both leads in during the first act. A two-hander implies the script favors neither actor over the other, so if that's your goal, you're going to need to showcase the other character in Act One, even if they don't meet until Act Two.
However, if you were to tell the same story mostly from the student's perspective, I can imagine a scenario where the mentor character might not become a factor until the second act.
Do you have a reel? Have you directed anything in the past? If not, the odds of being trusted with the director's chair go down dramatically.
You also have to consider how badly people want to make your script. Sometimes if the spec is THAT hot and the director has some kind of reel to show for it, you might be lucky enough to find a company willing to toss some cash at it. It helps if the script is low-budget, though.
I've certainly heard of more than one instance of music video or commercial directors writing their feature debut and holding out until someone allows them to direct. Bear in mind that in these cases, the scripts were so hot that they were being offered an additional half-million to a million dollars to cede the director's chair to someone else.
If you've got a low-budget script that you are determined to direct, your best bet is probably to finance it independently. You're probably not going to be dealing with many major production companies with something that small anyway.
And finally... "S" asks:
I writing in regards to ask for your insights as a professional reader. If screenplay structure and page count aren't a factor, are screenplays being judged on brevity of word count on the page? If the script doesn't facilitate a quick read is that a negative against the writer. And lastly if a work of fiction contains factual information be it medical, scientific, or police procedure that the reader isn't familiar with, should that be a critique against the writer? Thank you for reading and choosing to respond.
Okay, this is one of those questions where I can only say, "you're worrying about the wrong stuff."
"If screenplay structure and page count aren't a factor" - there is no world in which those aren't a factor. Page count directly relates to pacing and flow of the story. Structure is the backbone of the story. You will never find a reader who completely ignores structure and/or pacing in their evaluations - because you'll never find an executive who ignores both. Those are two of the more critical aspects of evaluating a script and a writer.
"Are screenplays being judged on brevity of word count on the page?" Indirectly. Scripts that are harder to read tend to be judged more harshly. If the reader has to keep rereading overwritten paragraphs so they can figure out just what exactly is going on in the story.
Brevity of word count is less of an issue than clarity of word count.
"If a script doesn't facilitate a quick read, is that a negative against the writer." Yes. Execs, readers, reps, they're all busy people with a lot to read. Never count on getting the benefit of the doubt so take great care when crafting your script to ensure that everything is clear and easy to understand.
"And lastly if a work of fiction contains factual information be it medical, scientific, or police procedure that the reader isn't familiar with, should that be a critique against the writer?"
It's a critique against the writer if they aren't able to make that information accessible to their audience. I had no medical training, but I was able to understand ER from the time I started watching at age 14. Few viewers had much insight into the process of collecting crime scene evidence before CSI, but that didn't prevent the series from making it accessible.
I'm sure many people see movies about subjects they aren't well-versed in. A good movie is able to help an audience understand without seemingly pandering or over-explaining at every turn.