Wouldn't "These bikes are modern and efficient" be okay?
No, that is backwards. The original sentence is talking about what "these" are, not what "these bicycles" are like.
Bikes is also correct
Since when isn't "bike"accepted?
Since this course launched, I guess. :) Please keep reporting.
Would "ezek a" be correct here too?
No.
ezek a modern biciklik = these modern bikes (or: these are the modern bikes)