EGR & MAF question

[grounch]

Hi
When i bought my X5 it had a P0101 + P0113, so MAF issue. Before buying a new one i went to check how it was installed there and...it was unplugged
So i plugged it back, and the reading went ok, cleaned the code and it didn't came back.
But the "orange triangle with circled arrow" light was still on.

So i read the codes again and now i have a P0401, which is EGR flow related.
The EGR valve is here, took a photo, then while looking on google to compare i noticed it's missing the small hose on it's "head".





The car behaves ok, no limp mode, no weird rev, pulls well.

The only thing is some white smoke cloud coming at cold startup, but don't know if it's related (if someone can tell me why it does that...). No smoke when starting warm, neither when flooring it.

What to do with this egr? Remove it for a cleaning?
Then what about this small hose that's not here? What's it's purpose, and also is it bad to drive like this?


Another thing: the check engin light never come in, even when they all light when i turn the key in the ignition. Should it light or not?


Thanks