In the same First Test Run, the Stealth Fighter seems to behave different way than described.

Our mistake. The Stealth Fighter card should have speed of 3 instead of 4. We are sorry; this is the only error on the cards we are aware of.

The game works with that, but the Stealth Fighter is a bit stronger than we intended. If you want the game to be better balanced, just rewrite the speed to 3 using a black marker. We will probably print the correct version of card with reprint or expansion.

Rulebook says you can choose any position for Androids, while Handbook says they play after the players. What is correct?

The Rulebook is correct. After the final testings, we decided to let the positon of androids up to the crew; unfortunately, the Handbook does not reflect this change.