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[The Fifth Horseman]

1. How many soldiers do I need in each base? I've found that six soldiers is the optimum for most missions, but I often suffer injuries.

I tend to use large numbers of troops, usually as many as I can pack onto the mission.

2. Research is way different. How many scientists/engineers do you suggest I should hire?

As many as you can stuff in your labs. If one much better then your worst one appears, sack the worst one and hire the new. You might want to keep some more skilled (90+ skill level) ones, for future labs.

3. Do androids gain experience? It says they improve "very slowly". However, my most senior officer is an android and hasn't improved even 1 point in any skill!

They don't improve. They do, however, score kills and missions - that's on what their promotions are based.

4. Are mutants and psychic powers worth it? It seems almost all aliens have very high resistance or immunity to psionics.

Nope. It all depends on the species - some just aren't conscious enough to be affected.

5. How do I IMPROVE relations with organizations without bribery? Is there any benefit to being allied with an organization?

Fight with their enemies. The relations will slowly rise. There are some benefits, but none too obvious.