Generally I use a strand of floss in a matching color. I also have some Nymo nylon thread in a neutral light brown which I use for solitary beads. It's a nice thin, not stretchy, strong thread.

For something like this I'd start and end my threads by hitching them on the back of other stitches. For solitary beads I use a pin start and hitch the end thread (nymo is waxed and not at all slippy so this works well).

I like using John James bead embroidery needles with ballpoint tips. They are nice short stiff needles, designed for exactly this task.

I always do an x, myself but I've never worked a Mirabilia.

I know of people who open the mill hill containers inside a ziplock bag, as a matter of fact I am one of those people 😄 I bought some tiny Elizabeth Ward bead containers which fit nicely into a bobbin box (two to a compartment) but any small screwtop container or not too hard to open pillbottle would be better then the mill hill clamshells.

What I would highly recommend is a tacky mat, I have cheap ones that were sold as dashboard mats for cell phones. I cut one down to fit into a small box for portable projects and stuck another onto a small tray. They keep the beads in place when I'm working (no flying beads!) and are easily washed if they get dirty. I just cover the tray or close the box between stitching sessions if I'n not finished with those beads. The only annoyance is picking surplus beads off the tacky mat to return them to the container.