Is technically possible to use road crank on a mountain bike?
What kind of BB do I need for Shimano Ultegra or SRAM Rival road crank to replace my 07 Giant Yukon crank/BB?

You will almost certainly encounter chainstay interference with both the crank arms and the inner chain ring if you try using an external bearing type BB which cannot be adjusted for width.
If you use an older style square taper or Octalink, you have a chance by using a longer spindle.
You need a wider chainline anyway on an MTB than you will achieve with an external type road crankset.
The next issue you will face is getting a road derailleur to adjust out to work with a 50mm chainline. Some might do it, and some might not.

Thanks for the reply.
I was planning to use SRAM mtb 10 speed rear derailleur with SRAM road shifters.
Something similar to this https://velonews.competitor.com/2009/...top-fuel_96645.

Pretty much the only thing I need to figure out is the crank/bb and the FD. I can also use SRAMs 10 speed MTB crank/FD however that would add an additional cost to my project as I already have Ultegra and Rival road cranks available.

Interesting. I didn't want to come off as completely negative on the idea. I have done a couple of similar conversions in the past and my comments were based on my experiences.
It can be doable, but I'd look into the Q factor of the cranks and check the width across your chainstays before putting out the dough.
Also, this setup will result in a poor chainline, so you would need to be extra vigilant about cross chaining from the inner chain ring, not so much from the outer.

Could not really tell from the pics, but for an external BB, you may have a problem. Road cranks are sized for 68mm BB shell, and MTB BB shell is normally 73mm wide. I ran into this trying to use a DA triple on a MTB frame. You might consider having your LBS face the BB shell to 68mm width (if you want to make it PERMANENT). I ended up using a different crank.

Not always. Not even usually. Most MTBs are 68mm, 73mm is less common, but it certainly is something to check for.
5mm is a heck of a lot of material to remove with a facing mill.

certainly other ways to get a 39/30 chainring combination, like a 110/74 Mtb triple ..
or an Ultegra triple, octalink or gasp, square taper BB.
with a chain guard instead of outer ring..
2/3rds of a triple

I have one mountain bike trek 830 26" wheels. Now have crank 48/38/28. and 7 speeds freewheel 13-30. My top speed is go less than road bikes? If i put crank 53/39 and 9 speeds casete 12-25 my mountain bike is go have speed same or close to road bikes? Does anyone there have try that setup in mountain bike?

How many times do we have to tell you that the gears aren't what make a bike "fast" or "slow" before it'll sink in? You can ask the same question over and over all you want, but it won't change that fact.

I have some spare parts and i wanted tried that setup. Now that is truth the legs is be fast or not is not the bike or gears.