1. Some researchers have argued that we learn most of the grammar we needed by the time we finish junior high school. The sentence is correct. "Would have learned" would be nonsense. 2. Last week we RECEIVED several complaints about problems with products sent to customers. You can't use the present perfect here. "Sent out" would also be incorrect. We are not concerned with the dispatching, or sending out, of products. We are only concerned with the products.

Both sentences have errors. 1. Some researchers have argued that we learn most of the grammar we needed by the time we finish junior high school. The best correction would be: ... that we learn most of the grammar we NEED by the time we finish junior high school. You can also say: ... that we HAVE LEARNED most of the grammar we NEED by the time we finish junior high school. If you want to use "needed", then you would use "would have learned" like you said: ... that we WOULD HAVE LEARNED most of the grammar we NEEDED by the time we finish junior high school. 2. Last week we have received several complaints about problems with products sent to customers. You can say "sent" or "sent out" - they have the same meaning. The error is in the first part. It should be simply "Last week we received several..." Last week we received several complaints about problems with products sent (out) to customers.