Is it possible to unlock all intimidate options and the special renegade mission in Mass Effect 1 while keeping most story related people alive?

So firstly, in order to unlock UNC: The Negotiation, you need to have 80% Renegade, or 90% Renegade if you had got to 80% Paragon first. Getting to 80% Renegade also unlocks the additional tiers of Intimidate and being a Spectre unlocks the remainder.

Now, starting at the beginning - I don't really want to reproduce the whole of this excellent guide here as that breaks down every choice in the game and assigns points to it already.

The first thing to note is your character backstory gives you renegade and paragon points. The most appropriate combination for maximum renegade points is Earthborn/Ruthless. Generally stay away from being a war hero as that gives you lots of paragon to start the game with.

The second thing to really consider is who you want to live. Are you trying to save the awesome characters that reappear later in the story in a meaningful way? What I'm asking here is do you mind collateral damage where it doesn't matter? Does Jeong from Exogeni need to live? How do you feel about killing a bunch of Thorian enslaved village folk?

Certain choices like killing Wrex have alternate Renegade options (like intimidating Wrex "Don't be so naive") which are also Renegade options but don't result in the death and still pile on the renegade points but other actions like saving the people of Feros are only going to pile on the paragon points. Saving the Rachni is always going to pile on loads of paragon points.

Finally is your play order. Depending on the choices you've made about who you're going to save decides on the order you're going to play the game in order to maximise your renegade points before you start piling on paragon points by saving the people you want to save. If you're saving the Rachni, delay Noveria as long as possible. As mentioned you can save Wrex with a renegade option without killing him, etc. As mentioned at the start of my answer you really want to reference this guide and plan your playthrough so you know which choices you can get away with while keeping the people you want to save alive.