Near to UAC Base is the starting map of Prodoomer, which you must complete before you can travel to the orbital city for the first time.
1. There is a cave containing a crossbow on the opposite side of the forest from where you enter. You can't miss it.
2. After getting the dynamite, check the walls in front of the cage for a passage to a teleporter that takes you back to the demolition site.
Once you have the ability to grenade + mine jump, check the high ledges in the forest for hidden indentations. There are two on the north ledge and one on the south. These are actually switches if you crouch and activate them, and they open up a passage in the southeast tunnel. Follow it to the end for a cutscene.
01 This ring is on the high ledge north of the waterfalls, on the northeast side of the forest. You can reach it by straferun jumping from the platform with the two kamikazes onto a very thin ledge on the wall to the north.
02 This is the ring you should have already picked up in secret #1.
If you're going for the achievement DASH IS 2FAST you can bypass almost the entire level by running to the corner where the waterfall and land intersect and mine + grenade jumping up the waterfall. Sprint past the enemies (Invisibility or Freeze Time help) jump off the edge past the ice lizard, jump over the fighting marines, and get to the exit.