Can party member go abroad?

Some party member can't apply for passports by individuals, but must be handled by the organization department. Passports are in their own hands unless necessary, and the rest of the time is managed by the organization department (generally cadres at or above the division level, depending on the regulations).

However, if you are an individual or private enterprise in party member, or just a recent graduate, just apply for a passport directly. The passport is in your own hands. Going abroad is exactly the same as going to party member.

Yes, party member does not affect going abroad. As long as you don't disclose and mark party member's identity when you go abroad, there is no rigid requirement to state your identity. Under normal circumstances, the competition for studying abroad does not consider political status, but needs ability and achievement, so don't worry about it. Write if party member's identity is useful, and don't write if it's useless. Unless you want to apply for a green card or apply for immigration, party member status may have an impact.

If your job involves confidentiality, you may not be able to get out, but you still have to apply.