Question: Was any Super Sentai footage used in this movie?
Answer: No. All footage in this film is original to this production.
Question: So does Rita Repulsa die when she goes into space? It seems unlikely she could survive mainly without oxygen.
Answer: No, she's not dead. This show seems to be following similarly to the original TV show. In the show, she was in a stasis like state trapped in a "trash can" on the moon. After she escapes this prison, she sets up her evil base with Lord Zed on the moon and continues to attack Angel Grove and the Rangers from the Moon. So her being blasted towards the Moon at the end of this reboot is a set up for her establishing a similar base of operations like in the show in the sequels. If the sequels ever get out of development hell.
Question: How could whoever made Rita a ranger not tell she was evil? Did she become corrupt over time like those who possess the ring in Lord of the Rings?
Answer: Rita was a part of Zordon's original team, but she betrayed them in her search for the Zeo crystals. She even killed the original members of Zordon's team until only Zordon's remained.
Answer: Rita was originally a part of Zordon's power rangers, and she was the green ranger of the team, so she would still have it. Rita may have magical abilities that would explain how she was unable to be harmed from bullets. Either that or her suit is bullet proof.