The "burping" you describe MAY be normal back flow through one of the ports at the bottom of the master cylinder. All of my trucks do this. If you let up on the pedal very slowly it won't splash out, otherwise replace the fill cap each time you fill it. If "burped" aggressively, you may be introducing air into the system. You need to also be sure the master cylinder doesn't have air in it itself, so some people bench bleed the M/C before installation.
Don is correct about the hydrovac, it should be bled first. Start with the bleeder in the center of the unit, and do the one near the line outlet to the system, second. Then bleed your cylinders. You are correct about the possibility of leaking brake fluid into the vacuum cylinder of the hydrovac, so it looks like that is not the problem. Since you have found the drain port this would be a good time to lubricate the vacuum chanber. People have suggested using Marvel's Mystery Oil for this; use an ounce or two.
Kent