The distance from your planet to its sun is going to be the hardest one. It's not too hard to get the relative distances of all of the planets, but you still need to set the scale (i.e., you can get all distances in AU, but you don't know how big an AU is). You can get an extremely imprecise (as in, the error bars are likely to include infinity) estimate from the angle between a moon and the Sun at exactly half-moon, but that's a difficult measurement (and depends on you even having a moon, which you might not). If you have a telescope and can observe the moons of some other planet, and know the speed of light, you can try using Ole Roemer's observation in reverse, but Roemer's observations were only good to within about 50%. Beyond that, it's either invent very good chronometers and wait for an inner planet to transit (if you have any inner planets), or invent radar powerful enough to reach across worlds.

For the mass of your planet, it's much easier to use one pendulum to get g (the gravitational field), and measure the planet's size using the shadows method. And if you're really paranoid about the possibility that G (Newton's constant) might be different, you'll need to repeat the Cavendish experiment (measuring the force between a couple of cannonballs in the laboratory); for any other experiment you conduct, all you'll ever find will be the product of G and some astronomical mass.