I'll start with the jungle desaster as the ladder stuff are basically follow-ups.
Sure, whenever you see some alien, first check whether it is looking into your direction. The radar map can be helpful, albeit it's not needed in 2.5. If it is, spend as little time in its field of view as possible, as you have to expect reaction fire, especially if it's the first turn. I probably would have scouted a little more, taking care not to trigger RF, then record the alien positions in my mind, and then throw a smoke grenade out of inside the dropship, because that action may also trigger RF. Then inside the smoke it's safe to move and to shoot from. Machine gun full auto at close range vs the sheevar should be a safe thing. Alternatively, RF can be disabled by a flashbang as well, but you may be forced to throw the flashbang out of smoke anyway as it can trigger RF as well.
So, typically, the very first action should be launching a smoke grenade, if only to make it possible to leave the dropship at all without immediate RF. It always depends on how many aliens are looking into your direction. Sometimes you're lucky and they are right beside you but facing another direction, then you can just shoot right away.
It may also help to know the TUs the alien weapon RF needs, without pistols, it's always 8 for plasma rifles and blasters. To avoid RF, only 7 spent TUs are allowed before leaving the field of view, such as by entering smoke. The TUs needed to leave the field of view no longer count.
EDIT
About missing at 99%: Sometimes you're just that unlucky, but other times the numbers lie at you. Can happen if stuff is in the way. If you repeatedly seem to miss (some of the full auto shots really shout go through at high chance to hit), change strategy. For instance, grenades most of the time do some damage at least thanks to their area damage. And if the sheevar is still not dead, think about what it'll want to do its next turn - likely move towards you, so put a fire field in between.