97 Intrepid wiper and headlight problem

Have 2 seperate problems with my 97 Intrepid, but maybe they are related.

The bright headlights came on without the switch being turned on, and would not shut off. Then after a few moments they went off on their own, and now I have no daytime running lights at all. The head lights work fine, in both high and low beam though. I found the drl fuse in the power centre was blown, so I replaced it. Immediately the highbeam lamps came back on, without no keys, or switch turned on! So for now I have unplugged the fuse.

2nd part is weird too.
Since then, my wipers only work is a really slow mode, slower than normal even. No high, low or intermediate speeds, just slower than slow.
I changed the wiper speed relay, no success, still the same.

Are the two systems hooked into the same possible control mod, and where is it located on the car?