Could use some fresh eyes and expertise on my son's e36 headgasket

I bought my son his first car, a non-running e36 that was stated to have a blown headgasket.

There are all the telltail signs of a blown head gasket but the actual gasket does not look to me to have any breached areas. It does not look to be in great condition, could this be enough to get water into the pistons? At this point the head does not seem to be warped. 

also the block seems to have a little electrolysis (circled area) can this be easily fixed? 

Here are some images for review 

Thanks!

Teenagers 

some blue devil for ya?

I thought bmw plastic cooling system craps out, car overheats and warps or cracks the head is a common scenario.  Which means replace the whole cooling system while you are at it.  

How did you check the head? It needs to be checked and pressure tested.  The six head is like a mile long so they like warping.  

Cool car, good luck with it.  

I did the straight edge and feeler gauge test to the head. I looks to be not warped. 

Check the block.  They can warp too.

I have had heads corrode out from under the fire ring as well.  On that picture of the head, look real close at the fire ring to coolant passage areas at the end cylinders on the left side of the picture, towards the front/rear of the head.  They look pretty dark and are awful close to combustion.