Local indexes vs Global indexes for partitioned tables in Oracle
…does partitioning alleviates slowness with inserts and updates or partitioning indexes is enough to guarantee a faster insert and update…Does it make sense to partition tables to speed up inserts?


No, absolutely not. The primary benefit of partitioning is the low cost of dropping partitions. You said "data can be archived or discarded a few weeks later", which might make you a genuine candidate for partitioning.


  Is it optimal to define local indexes on the unique id or is it better to define global indexes and partition them as I have already done?…What are the downsides of having global partitioned indexes for constantly growing data? Once I decide to remove the partitions at a later point of time, since the indexes are not partitioned by timestamp but instead by unique id, will the operation cause a direct impact on functioning indexes?


Using global indexes goes against the grain of partitioning in the first place — they are marked 'unusable' if you drop a partition.

You may find this ORACLE-BASE article a useful read.