When I added new link between SW1 and SW3, Fa0/2 and Fa0/1interfaces of SW3 became Alternate Ports. I think Fa0/2 of SW3 should have not been an Alternate Port because in the segment between SW4 and SW3, Fa0/2 interface of SW3 should have been DP for SW3 has Lower BID than SW4. Thus, actual Alternate Port should have been Fa0/1 interface of SW4.
What's wrong with me ?
Looks like the reason why stp calculated best path to root bridge for sw 3 via that direct path to sw1 was sw1 was already designated root bridge, So the next order of preference in stp calculation would be root path cost (RPC) as sw3 now has a direct link to sw1 this was chosen a designated/root with sw2/4 having their own lower rpc link to the root bridge. Sw3 two links to either switch 2-4 were put into alternate state seems to suggest both of those switches (sw2 having a lower bid, sw4 having a higher bid of sw3).
I agree. Assuming no priority has been configured anywhere, SW4 Fa0/1 should go alternate based off of lowest mac. Can you paste the outputs of show spanning tree from SW3 and SW4?
Hope that helps!