Is Ethernet synchronous or asynchronous serial?
I think you're getting multiple answers, because the real answer is that you can't quite wedge what the various flavors of Ethernet are into the definitions of &quot;synchronous serial&quot; or &quot;asynchronous serial&quot;.  In fact, not all Ethernet flavors are entirely serial, because they involve parallel wires.

Ethernet has no separate wire for clock signal, so does it make it asynchronous?
But Ethernet also does not use start and stop bits, so does it make it synchronous?

Most Ethernet flavors have framing bits, that establish both the start of the frame and that prime the bit timing recovery circuitry of the receivers.  You could, given enough beer, convince me that these are &quot;just start and stop bits&quot; -- but after I sobered up, I may no longer agree.
Ditto convincing me that they cannot be start and stop bits.

And by the way, can we encapsulate Ethernet into RS-232? That is, can we use RS-232 to carry or transport Ethernet?

In a sense, yes.  You could design a protocol that would encapsulate Ethernet frames and send them via RS-232.  Or semaphore, if you could find a patient enough pair of sailors.  Or just about any other sufficiently flexible means of transmitting digital information.  Delay would be an issue, so you'd probably need something that acts more like a switch than a bridge.
Since most Ethernet communications is using Internet Protocol, your best bet is to not try to wrap Ethernet in serial, but rather to use PPP, which is well-established, solid, and just works.